Relevant bibliographies by topics / Semi linear equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Semi linear equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Semi linear equation"

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Wang, Feizhi, and Yisheng Huang. "On a semi-linear Schrödinger equation in." Nonlinear Analysis: Theory, Methods & Applications 62, no. 5 (August 2005): 833–48. http://dx.doi.org/10.1016/j.na.2005.03.087.

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Krieger, J., and W. Schlag. "On the focusing critical semi-linear wave equation." American Journal of Mathematics 129, no. 3 (2007): 843–913. http://dx.doi.org/10.1353/ajm.2007.0021.

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Bokanowski, Olivier, Athena Picarelli, and Christoph Reisinger. "Stability and convergence of second order backward differentiation schemes for parabolic Hamilton–Jacobi–Bellman equations." Numerische Mathematik 148, no. 1 (May 2021): 187–222. http://dx.doi.org/10.1007/s00211-021-01202-x.

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AbstractWe study a second order Backward Differentiation Formula (BDF) scheme for the numerical approximation of linear parabolic equations and nonlinear Hamilton–Jacobi–Bellman (HJB) equations. The lack of monotonicity of the BDF scheme prevents the use of well-known convergence results for solutions in the viscosity sense. We first consider one-dimensional uniformly parabolic equations and prove stability with respect to perturbations, in the $$L^2$$ L 2 norm for linear and semi-linear equations, and in the $$H^1$$ H 1 norm for fully nonlinear equations of HJB and Isaacs type. These results are then extended to two-dimensional semi-linear equations and linear equations with possible degeneracy. From these stability results we deduce error estimates in $$L^2$$ L 2 norm for classical solutions to uniformly parabolic semi-linear HJB equations, with an order that depends on their Hölder regularity, while full second order is recovered in the smooth case. Numerical tests for the Eikonal equation and a controlled diffusion equation illustrate the practical accuracy of the scheme in different norms.
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Mahomed, F. M., A. Qadir, and A. Ramnarain. "Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods." Mathematical Problems in Engineering 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/202973.

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In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs) in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semi-invariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting a complex scalar ordinary differential equation (ODE) into its real and imaginary parts PDEs for two functions of two variables were obtained and their symmetry structure studied. In this work we revisit semi-invariants under equivalence transformations of the dependent variables for systems of two linear hyperbolic PDEs in two independent variables when such systems correspond to scalar complex linear hyperbolic equations in two independent variables, using the above-mentioned splitting procedure. The semi-invariants under linear changes of the dependent variables deduced for this class of hyperbolic linear systems correspond to the complex semi-invariants of the complex scalar linear hyperbolic equation. We show thatthe adjoint factorization corresponds precisely to the complex splitting. We also study the reductions and the inverse problem when such systems of two linear hyperbolic PDEs arise from a linear complex hyperbolic PDE. Examples are given to show the application of this approach.
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ANH, CUNG THE, and TANG QUOC BAO. "PULLBACK ATTRACTORS FOR A NON-AUTONOMOUS SEMI-LINEAR DEGENERATE PARABOLIC EQUATION." Glasgow Mathematical Journal 52, no. 3 (August 25, 2010): 537–54. http://dx.doi.org/10.1017/s0017089510000418.

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AbstractIn this paper, using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semi-linear degenerate parabolic equation in an arbitrary domain, without restriction on the growth order of the polynomial type non-linearity and with a suitable exponential growth of the external force. The obtained results improve some recent ones for the non-autonomous reaction–diffusion equations.
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Yin, Zhongqi. "Lipschitz stability for a semi-linear inverse stochastic transport problem." Journal of Inverse and Ill-posed Problems 28, no. 2 (April 1, 2020): 185–93. http://dx.doi.org/10.1515/jiip-2018-0115.

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AbstractThis paper is addressed to a semi-linear stochastic transport equation with three unknown parameters. It is proved that the initial displacement, the terminal state and the random term in diffusion are uniquely determined by the state on partial boundary and a Lipschitz stability of the inverse problem is established. The main tool we employ is a global Carleman estimate for stochastic transport equations.
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Avdonin, S. A., B. P. Belinskiy, and John V. Matthews. "Inverse problem on the semi-axis: local approach." Tamkang Journal of Mathematics 42, no. 3 (August 24, 2011): 275–93. http://dx.doi.org/10.5556/j.tkjm.42.2011.916.

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We consider the problem of reconstruction of the potential for the wave equation on the semi-axis. We use the local versions of the Gelfand-Levitan and Krein equations, and the linear version of Simon's approach. For all methods, we reduce the problem of reconstruction to a second kind Fredholm integral equation, the kernel and the right-hand-side of which arise from an auxiliary second kind Volterra integral equation. A second-order accurate numerical method for the equations is described and implemented. Then several numerical examples verify that the algorithms can be used to reconstruct an unknown potential accurately. The practicality of each approach is briefly discussed. Accurate data preparation is described and implemented.
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Castro, Hernán. "Oscillations in a semi-linear singular Sturm–Liouville equation." Asymptotic Analysis 94, no. 3-4 (September 16, 2015): 363–73. http://dx.doi.org/10.3233/asy-151318.

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Oghre, E. O., and B. I. Olajuwon. "Fourier Transform Solution of the Semi-linear Parabolic Equation." Journal of Applied Sciences 5, no. 3 (February 15, 2005): 492–95. http://dx.doi.org/10.3923/jas.2005.492.495.

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V. Lê, Út. "Contraction-Galerkin method for a semi-linear wave equation." Communications on Pure & Applied Analysis 9, no. 1 (2010): 141–60. http://dx.doi.org/10.3934/cpaa.2010.9.141.

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Dissertations / Theses on the topic "Semi linear equation"

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Michalk, Linda [Verfasser]. "Semi-Analytical Semi-Lagrangian Discontinuous Galerkin Advection Scheme for the Compressible Linear Advection Equation / Linda Michalk." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1176707140/34.

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Oswald, Luc. "Etude de problemes non lineaires avec singularites." Paris 6, 1987. http://www.theses.fr/1987PA066060.

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Cette these est composee de dix articles que nous avons regroupes en deux parties. La premiere partie est constituee par l'etude et la classification des singularites isolees, premierement, d'une equation elliptique avec diffusion, deuxiemement, de l'equation parabolique correspondante. Dans la seconde partie sont etablis des resultats d'existence pour des problemes elliptiques semi-lineaires. Ces problemes sont caracterises respectivement, par une non-linearite singuliere, une condition de neumann degeneree, une non-linearite sous lineaire et, enfin, des exposants de sobolev critiques
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Bouchitte, Guy. "Calcul des variations en cadre non reflexif : representation et relaxation de fonctionnelles integrales sur un espace de mesures, applications en plasticite et homogeneisation." Perpignan, 1987. http://www.theses.fr/1987PERP0033.

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Etude variationnelle de fonctionnelles convexes du type somomega f(x,u(x),du)dx lorsque la croissance de f necessite du travail dans un banach non reflexif. On abordera en particulier les questions relatives a la semi-continuite inferieure, la relaxation, la convergence variationnelle et l'approximation, l'equation d'euler. . . Ayant en vue certaines applications dans le dommaine de la mecanique (plasticite, milieux fissures), on s'interessera principalement au cas ou l'integrande f presente une croissance lineaire par rapport au gradient. Suivant une demarche desormais classique, cela nous amenera a etendre la definition de la fonctionnelle a des fonctions dont le gradient est une mesure bornee (espaces de type bv(omega ) ou bd(omega ). Dans cette optique, une contribution substanstielle est apportee (chapitres ii et iii notamment) au probleme de la relaxation sur un espace de mesures d'une fonctionnelle integrale dependant du parametre. Les 3 derniers chapitres ont une connotation beaucoup plus "appliquee" et sont consacres a quelques problemes d'homogeneisation et d'analyse limite issus des equations de la plasticite (chapitre v) ou de l'etude des phenomenes de diffraction en electromagnetisme (chapitre vi et vii)
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Bui, Tang Bao Ngoc. "Semi-linear waves with time-dependent speed and dissipation." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-147037.

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The main goal of our thesis is to understand qualitative properties of solutions to the Cauchy problem for the semi-linear wave model with time-dependent speed and dissipation. We greatly benefited from very precise estimates for the corresponding linear problem in order to obtain the global existence (in time) of small data solutions. This reason motivated us to introduce very carefully a complete description for classification of our models: scattering, non-effective, effective, over-damping. We have considered those separately.
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Cherfils, Laurence. "Méthode de cheminement adaptative pour les problèmes semi-linéaires dépendant d'un paramètre." Université Joseph Fourier (Grenoble), 1996. http://www.theses.fr/1996GRE10105.

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Ce travail consiste en l'élaboration d'une méthode de cheminement, dite également méthode de continuation, destinée aux problèmes de bifurcation qui apparaîssent lors de la discrétisation par éléments finis P1 d'une EDP semi-linéaire dépendant d'un paramètre. Afin de construire une méthode suffisamment robuste pour traiter les problèmes dont les solutions présentent des phénomènes de couches limites ou de singularités, nous avons intégré à la méthode de cheminement introduite par E. L. Allgower et K. Georg des techniques d'éléments finis adaptatifs, ainsi qu'une implémentation parallèle sur un réseau de stations, afin de diminuer les besoins en place mémoire et le temps de calculs nécessaires à l'évaluation d'une branche entière de solutions de bonne précision. Dans le cas de problèmes mono-dimensionnels, des essais sont effectués pour améliorer la qualité de la solution en déplaçant les nœuds du maillage, afin d'éviter le recours au raffinement. Enfin, sur un exemple où la singularité des solutions est dûe à la géométrie du domaine sur lequel est posé l'EDP, nous montrons comment l'utilisation d'un maillage «adapté à la singularité» permet de pallier le manque de régularité. On obtient en effet, pour la norme H1, une convergence optimale des branches de solutions approchées vers les branches de solutions exactes
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Eslick, John. "A Dynamical Study of the Evolution of Pressure Waves Propagating through a Semi-Infinite Region of Homogeneous Gas Combustion Subject to a Time-Harmonic Signal at the Boundary." ScholarWorks@UNO, 2011. http://scholarworks.uno.edu/td/1367.

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In this dissertation, the evolution of a pressure wave driven by a harmonic signal on the boundary during gas combustion is studied. The problem is modeled by a nonlinear, hyperbolic partial differential equation. Steady-state behavior is investigated using the perturbation method to ensure that enough time has passed for any transient effects to have dissipated. The zeroth, first and second-order perturbation solutions are obtained and their moduli are plotted against frequency. It is seen that the first and second-order corrections have unique maxima that shift to the right as the frequency decreases and to the left as the frequency increases. Dispersion relations are determined and their limiting behavior investigated in the low and high frequency regimes. It is seen that for low frequencies, the medium assumes a diffusive-like nature. However, for high frequencies the medium behaves similarly to one exhibiting relaxation. The phase speed is determined and its limiting behavior examined. For low frequencies, the phase speed is approximately equal to sqrt[ω/(n+1)] and for high frequencies, it behaves as 1/(n+1), where n is the mode number. Additionally, a maximum allowable value of the perturbation parameter, ε = 0.8, is determined that ensures boundedness of the solution. The location of the peak of the first-order correction, xmax, as a function of frequency is determined and is seen to approach the limiting value of 0.828/sqrt(ω) as the frequency tends to zero and the constant value of 2 ln 2 as the frequency tends to infinity. Analytic expressions are obtained for the approximate general perturbation solution in the low and high-frequency regimes and are plotted together with the perturbation solution in the corresponding frequency regimes, where the agreement is seen to be excellent. Finally, the solution obtained from the perturbation method is compared with the long-time solution obtained by the finite-difference scheme; again, ensuring that the transient effects have dissipated. Since the finite-difference scheme requires a right boundary, its location is chosen so that the wave dissipates in amplitude enough so that any reflections from the boundary will be negligible. The perturbation solution and the finite-difference solution are found to be in excellent agreement. Thus, the validity of the perturbation method is established.
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Nascimento, Wanderley Nunes do. "Klein-Gordon models with non-effective time-dependent potential." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7453.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.
Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes.
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Mtiraoui, Ahmed. "I. Etude des EDDSRs surlinéaires II. Contrôle des EDSPRs couplées." Thesis, Toulon, 2016. http://www.theses.fr/2016TOUL0010/document.

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Cette thèse aborde deux sujets de recherches, le premier est sur l’existence et l’unicité des solutions des Équations Différentielles Doublement Stochastiques Rétrogrades (EDDSRs) et les Équations aux Dérivées partielles Stochastiques (EDPSs) multidimensionnelles à croissance surlinéaire. Le deuxième établit l’existence d’un contrôle optimal strict pour un système controlé dirigé par des équations différentielles stochastiques progressives rétrogrades (EDSPRs) couplées dans deux cas de diffusions dégénérée et non dégénérée.• Existence et unicité des solutions des EDDSRs multidimensionnels :Nous considérons EDDSR avec un générateur de croissance surlinéaire et une donnée terminale de carré intégrable. Nous introduisons une nouvelle condition locale sur le générateur et nous montrons qu’elle assure l’existence, l’unicité et la stabilité des solutions. Même si notre intérêt porte sur le cas multidimensionnel, notre résultat est également nouveau en dimension un. Comme application, nous établissons l’existence et l’unicité des solutions des EDPS semi-linéaires.• Contrôle des EDSPR couplées :Nous étudions un problème de contrôle avec une fonctionnelle coût non linéaire dont le système contrôlé est dirigé par une EDSPR couplée. L’objective de ce travail est d’établir l’existence d’un contrôle optimal dans la classe des contrôle stricts, donc on montre que ce contrôle vérifie notre équation et qu’il minimise la fonctionnelle coût. La méthode consiste à approcher notre système par une suite de systèmes réguliers et on montre la convergence. En passant à la limite, sous des hypothèses de convexité, on obtient l’existence d’un contrôle optimal strict. on suit cette méthode théorique pour deux cas différents de diffusions dégénérée et non dégénérée
In this Phd thesis, we considers two parts. The first one establish the existence and the uniquness of the solutions of multidimensional backward doubly stochastic differential equations (BDSDEs in short) and the stochastic partial differential equations (SPDEs in short) in the superlinear growth generators. In the second part, we study the stochastic controls problems driven by a coupled Forward-Backward stochastic differentialequations (FBSDEs in short).• BDSDEs and SPDEs with a superlinear growth generators :We deal with multidimensional BDSDE with a superlinear growth generator and a square integrable terminal datum. We introduce new local conditions on the generator then we show that they ensure the existence and uniqueness as well as the stability of solutions. Our work go beyond the previous results on the subject. Although we are focused on multidimensional case, the uniqueness result we establish is new in one dimensional too. As application, we establish the existence and uniqueness of probabilistic solutions tosome semilinear SPDEs with superlinear growth generator. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.• Controlled coupled FBSDEs :We establish the existence of an optimal control for a system driven by a coupled FBDSE. The cost functional is defined as the initial value of the backward component of the solution. We construct a sequence of approximating controlled systems, for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we get the existence of a feedback optimal control. The convexity condition is used to ensure that the optimal control is strict. In this part, we study two cases of diffusions : degenerate and non-degenerate
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Maach, Fatna. "Existence pour des systèmes de réaction-diffusion ou quasi linéaires avec loi de balance." Nancy 1, 1994. http://www.theses.fr/1994NAN10121.

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Notre étude concerne des problèmes d'existence (ou de non-existence) pour des systèmes de réaction-diffusion elliptiques quasi linéaires présentant deux propriétés essentielles et fréquentes dans les applications, à savoir: 1) les solutions (éventuelles) sont positives; 2) la masse totale des composants est a priori contrôlée: ceci correspond à une propriété structurelle des termes non linéaires, par exemple que leur somme est négative ou nulle. Pour les systèmes semi-linéaires deux fois deux, c'est-à-dire lorsque les termes non linéaires sont indépendants des gradients et dans le cas ou l'un des composants est de plus a priori contrôlé, nous faisons une étude complète. Nous analysons en particulier l'influence des données au bord relativement à l'existence ou la non-existence des solutions. Nous montrons ainsi, moyennant certaines hypothèses, que pour la plupart des combinaisons de données au bord, on a existence. Des résultats négatifs sont donnés pour les autres types de données au bord. Quand les termes non linéaires dépendent des gradients et quand cette dépendance est sous-quadratique, nous obtenons l'existence de solutions classiques. Nous donnons également un résultat d'existence lorsque les données sont très peu régulières. Nous étudions enfin le cas de croissance quadratique ou sur-quadratique et nous montrons l'existence de solutions classiques si les operateurs de diffusions sont proportionnels
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Davidson, Bryan Duncan. "Recursive projection for semi-linear partial differential equations." Thesis, University of Bristol, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294932.

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Books on the topic "Semi linear equation"

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Melrose, Richard B. Semi-linear diffraction of conormal waves. Paris: Société mathématique de France, 1996.

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Melrose, Richard B. Semi-linear diffraction of conormal waves. Paris: Société Mathématique de France, 1996.

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Melrose, Richard B. Semi-linear diffraction of conormal waves. Paris: Société Mathématique de France, 1996.

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Haraux, Alain. Semi-linear hyperbolic problems in bounded domains. Chur: Harwood Academic Publishers, 1987.

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Zhao, Huaizhong. The stochastic elementary formula method and approximate travelling waves for semi-linear reaction diffusion equations. [s.l.]: typescript, 1994.

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Smolarski, Dennis Chester. An optimum semi-iterative method for solving any linear set with a square matrix. Urbana, Ill. (1304 W. Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1985.

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Meyer, J. C., and D. J. Needham. Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations. Cambridge University Press, 2015.

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Engel, Klaus-Jochen, and Rainer Nagel. One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics). Springer, 1999.

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Book chapters on the topic "Semi linear equation"

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Melliani, Said. "Semi-linear Equation with Fuzzy Parameters." In Lecture Notes in Computer Science, 271–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-540-48061-7_33.

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Rasulov, Abdujabbor, Gulnora Raimova, and Matyokub Bakoev. "Monte Carlo Solution of Dirichlet Problem for Semi-linear Equation." In Finite Difference Methods. Theory and Applications, 443–51. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_51.

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Bradji, Abdallah, and Moussa Ziggaf. "A Convergence Result of a Linear SUSHI Scheme Using Characteristics Method for a Semi-linear Parabolic Equation." In Advances in High Performance Computing, 452–62. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55347-0_38.

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Dozzi, M., E. T. Kolkovska, and J. A. López-Mimbela. "Finite-Time Blowup and Existence of Global Positive Solutions of a Semi-linear Stochastic Partial Differential Equation with Fractional Noise." In Modern Stochastics and Applications, 95–108. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03512-3_6.

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Triebel, Hans. "Truncations and Semi-linear Equations." In The Structure of Functions, 355–402. Basel: Springer Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-0569-8_4.

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Diagana, Toka. "Semi-Group of Linear Operators." In Semilinear Evolution Equations and Their Applications, 45–56. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00449-1_3.

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Abbas, Saïd, and Mouffak Benchohra. "Impulsive Semi-linear Functional Differential Equations." In Developments in Mathematics, 191–259. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17768-7_9.

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Triebel, Hans. "Semi-linear Equations; the Q-method." In The Structure of Functions, 389–402. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8257-6_27.

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Lantsman, M. H. "Power Order Growth Functions on the Positive Semi-Axis." In Asymptotics of Linear Differential Equations, 90–127. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9797-5_5.

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Lantsman, M. H. "Linear Differential Equations in Singular Cases on the Positive Semi-Axis." In Asymptotics of Linear Differential Equations, 273–306. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9797-5_11.

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Conference papers on the topic "Semi linear equation"

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Barron-Romero, Carlos. "On the controllability of a Cubic Semi-Linear Wave Equation." In 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2019. http://dx.doi.org/10.1109/codit.2019.8820332.

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Ramirez, Lynnette E. S., and Carlos F. M. Coimbra. "A Constitutive Equation for Linear Viscoelastic Thermoset Materials Undergoing Compression." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34169.

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A constitutive equation for linear viscoelasticity is presented. The equation is formulated using a Variable-Order (VO) integro-differential operator, in which the order of the derivative q(t*) is allowed to be a function of the dependent or independent variables. We propose a relationship in which the stress is related to the q-th derivative of strain, where q(t*) and the normalized time t* characterize the viscoelastic response of the material. We assume that the function q(t*) is a measure of the rate of change of disorder within the material and develop a statistical mechanical model. The resulting model correlates well with experimental results for strain rate values varying over eight orders of magnitude. Using experimental data for a carbon/epoxy composite and an epoxy resin undergoing constant rate compression in the linear range, we derive a semi-empirical functional relationship with the normalized time that is used in a VO constitutive equation to model the viscoelastic deformation in time. The resulting dimensionless constitutive equation requires a much smaller number of empirically determined coeffcients to adequately represent the data.
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Insperger, Tamás, and Gábor Stépán. "Semi-Discretization of Delayed Dynamical Systems." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21446.

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Abstract An efficient numerical method is presented for the stability analysis of linear retarded dynamical systems. The method is based on a special kind of discretization technique with respect to the past effect only. The resulting approximate system is delayed and time-periodic in the same time, but still, it can be transformed analytically into a high dimensional linear discrete system. The method is especially efficient for time varying delayed systems, including the case when the time delay itself varies in time. The method is applied to determine the stability charts of the delayed Mathieu equation with damping.
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Akkaya, Tugce, and Wim T. van Horssen. "On Boundary Damping for Semi-Infinite Strings and Beams." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50457.

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In this paper, initial boundary value problems for a linear string and beam equation are considered. The main aim is to study the reflection of an incident wave at the boundary and the damping properties for different types of boundary conditions such as a mass-spring-dashpot for semi-infinite strings, and pinned, sliding, clamped and damping boundary conditions for semi-infinite beams. The system of transverse vibrations are divided into model 1 and model 2 which are described as a string problem and beam problem, respectively. In order to construct explicit solutions of the boundary value problem for the first model the D’Alembert method will be used to the one dimensional wave equation on the semi-infinite domain, and for the second model the method of Laplace transforms will be applied to a beam equation on a semi-infinite domain. It will be shown how waves are damped and reflected for different types of boundaries and how much energy is dissipated at the boundary.
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Cai, Guang-Bin, Ling-Ling Lv, Hua-Feng He, and Tao Zhou. "Periodic Lyapunov equation based approach to semi-global almost disturbance decoupling of continuous-time periodic linear systems subject to input saturation." In 2015 34th Chinese Control Conference (CCC). IEEE, 2015. http://dx.doi.org/10.1109/chicc.2015.7259632.

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Rai, K. N., and D. C. Rai. "A Finite Element Method for the Solution of Free Boundary Problem." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56777.

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A finite element method is presented for the solution of a free boundary problem which arises during planar melting of a semi-infinite medium initially at a temperature which is slightly below the melting temperature of the solid. The surface temperature is assumed to vary with time. Two different situations are considered (I) when thermal diffusivity is independent of temperature and (II) when thermal diffusivity varies linearly with temperature. The differential equation governing the process is converted to initial value problem of vector matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied, a linear differential equation can be represented by a set of linear algebraic equations and a nonlinear differential equation can be represented by a set of nonlinear algebraic equations. The solution of the problem is then found in terms of Chebyshev polynomial of second kind. The solution of this initial value problem is utilized iteratively in the interface heat flux equation to determine interface location as well as the temperature in two regions. The method appears to be accurate in cases for which closed form solutions are available, it agrees well with them. The effect of several parameters on the melting are analysed and discussed.
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Wang, D. H., and W. H. Liao. "Semi-Active Suspension Systems for Railway Vehicles Based on Magnetorheological Fluid Dampers." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34776.

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In this paper, a seventeen degree-of-freedom (DOF) model for a full scale railway vehicle integrated with the semi-active controlled magnetorheological (MR) fluid dampers in its secondary suspension system is proposed to cope with the lateral, yaw, and roll motions of the car body, trucks, and wheelsets. The governing equation considering the dynamics of the railway vehicle integrated with MR fluid dampers in the secondary suspension system and the dynamics of the rail track irregularities are developed. The Linear Quadratic Gaussion (LQG) control law using the acceleration feedback is adopted, in which the state variables are estimated from the measurable accelerations with a Kalman estimator. In order to evaluate how the performances of the railway vehicle system integrated with the semi-active controlled MR fluid dampers can be improved, the lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full scale railway vehicle integrated with MR fluid dampers, which are controlled (the semi-active) and uncontrolled (the passive on and passive off) respectively, are analyzed under the random track irregularities based on the established governing equations and the modelled track irregularities. The simulation results not only show the control effectiveness of the railway vehicle with the semi-active suspension system based on MR fluid dampers for railway vehicles, but also illustrate that the semi-active railway vehicle suspension system based on MR fluid dampers combines the merits of the passive on and passive off railway vehicle suspension systems.
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8

Vlahostergios, Zinon, and Kyros Yakinthos. "Modeling Separation-Induced Transition Using a Non-Linear Three Equation Turbulence Model and a Reynolds Stress Turbulence Model." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23331.

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This paper presents an effort to model separation-induced transition on a flat plate with a semi-circular leading edge, by using two advanced turbulence models, the three equation non-linear model k-ε-A2 of Craft et al. [16] and the Reynolds-stress model of Craft [13]. The mechanism of the transition is governed by the different inlet velocity and turbulence intensity conditions, which lead to different recirculation bubbles and different transition onset points for each case. The use of advanced turbulence models in predicting the development of transitional flows has shown, in past studies, good perspectives. The k-ε-A2 model uses an additional transport equation for the A2 Reynolds stress invariant and it is an improvement of Craft et al. [12] non-linear eddy viscosity model. The use of the third transport equation gives improved results in the prediction of the longitudinal Reynolds stress distributions and especially, in flows where transitional phenomena may occur. Although this model is a pure eddy-viscosity model, it borrows many aspects from the more complex Reynolds-stress models. On the other hand, the use of an advanced Reynolds-stress turbulence model, such as the one of Craft [13], can predict many complex flows and there are indications that it can be applied to transitional flows also, since the crucial terms of Reynolds stress generation are computed exactly and normal stress anisotropy is resolved. The model of Craft [13], overcomes the drawbacks of the common used Reynolds-stress models regarding the computation of wall-normal distances and vectors in order to account for wall proximity effects. Instead of these quantities, it employs “normalized turbulence lengthscale gradients” which give the ability to identify the presence of strong inhomogeneity in a flow development, in an easier way. The final results of both turbulence models showed acceptable agreement with the experimental data. In this work it is shown that there is a good potential to model separation-induced transitional flows, with advanced turbulence modeling without any additional use of ad-hoc modifications or additional equations, based on various transition models.
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Rajaomazava, Tolotra Emerry, Mustapha Benaouicha, and Jacques-Andre´ Astolfi. "A Comparison Study of Coupling Algorithms for Fluid-Structure Interaction Problems." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57573.

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The influence of numerical schemes for solving coupled problem in fluid-structure interaction is addressed. A non-linear Burgers equation in a bounded domain with moving interface is solved by finite element method (FEM). The implicit and explicit coupling algorithms are studied with interface equation solved at outside then inside of Newton iterative procedure (referred to as implicit-outer, implicit-inner, explicit and semi-implicit schemes respectively). Iteration numbers and computing time are compared for each algorithm. The interface position and energy conservation condition at the interface are discussed.
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Insperger, Tama´s, Tony L. Schmitz, Timothy J. Burns, and Ga´bor Ste´pa´n. "Comparison of Analytical and Numerical Simulations for Variable Spindle Speed Turning." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41809.

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The turning process with varying spindle speed is investigated. The well-known single degree of freedom turning model is presented and the governing delay-differential equation with time varying delay is analyzed. Three different numerical techniques are used to solve the governing equation: (1) direct Euler simulation with linear interpolation of the delayed term, (2) Taylor expansion of the time delay variation combined with Euler integration and (3) semi-discretization method. The results of the three method are compared. Stability charts are constructed, and some improvements in the process stability is shown, especially for low spindle speed domains.
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Reports on the topic "Semi linear equation"

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Chandrasekaran, S., P. DeWilde, M. Gu, T. Pals, A. van der Veen, and D. White. Fast Stable Solvers for Sequentially Semi-Seperable Linear Systems of Equations. Office of Scientific and Technical Information (OSTI), January 2003. http://dx.doi.org/10.2172/15003389.

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