Relevant bibliographies by topics / Differential equations, Partial – Asymptotic theory

Contents

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

Academic literature on the topic 'Differential equations, Partial – Asymptotic theory'

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Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Differential equations, Partial – Asymptotic theory"

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Bandle, Catherine. "SOME ASYMPTOTIC PROBLEMS IN THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS (Lezioni Lincee)." Bulletin of the London Mathematical Society 30, no. 3 (May 1998): 326–27. http://dx.doi.org/10.1112/s0024609397274096.

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S., L. R., Hans G. Kaper, and Marc Garbey. "Asymptotic Analysis and the Numerical Solution of Partial Differential Equations." Mathematics of Computation 59, no. 199 (July 1992): 303. http://dx.doi.org/10.2307/2153003.

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Khodja, Farid Ammar, Assia Benabdallah, and Djamel Teniou. "Stability of coupled systems." Abstract and Applied Analysis 1, no. 3 (1996): 327–40. http://dx.doi.org/10.1155/s1085337596000176.

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The exponential and asymptotic stability are studied for certain coupled systems involving unbounded linear operators and linear infinitesimal semigroup generators. Examples demonstrating the theory are also given from the field of partial differential equations.
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RUDNICKI, RYSZARD, and KATARZYNA PICHÓR. "MARKOV SEMIGROUPS AND STABILITY OF THE CELL MATURITY DISTRIBUTION." Journal of Biological Systems 08, no. 01 (March 2000): 69–94. http://dx.doi.org/10.1142/s0218339000000067.

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A model of the maturity-structured cell population is considered. This model is described by a partial differential equation with a transformed argument. Using the theory of Markov semigroups we establish a new criterion for asymptotic stability of such equations.
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Hibino, Masaki. "Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type, II." Publications of the Research Institute for Mathematical Sciences 37, no. 4 (2001): 579–614. http://dx.doi.org/10.2977/prims/1145477330.

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Bouatta, Mohamed A., Sergey A. Vasilyev, and Sergey I. Vinitsky. "The asymptotic solution of a singularly perturbed Cauchy problem for Fokker-Planck equation." Discrete and Continuous Models and Applied Computational Science 29, no. 2 (December 15, 2021): 126–45. http://dx.doi.org/10.22363/2658-4670-2021-29-2-126-145.

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The asymptotic method is a very attractive area of applied mathematics. There are many modern research directions which use a small parameter such as statistical mechanics, chemical reaction theory and so on. The application of the Fokker-Planck equation (FPE) with a small parameter is the most popular because this equation is the parabolic partial differential equations and the solutions of FPE give the probability density function. In this paper we investigate the singularly perturbed Cauchy problem for symmetric linear system of parabolic partial differential equations with a small parameter. We assume that this system is the Tikhonov non-homogeneous system with constant coefficients. The paper aims to consider this Cauchy problem, apply the asymptotic method and construct expansions of the solutions in the form of two-type decomposition. This decomposition has regular and border-layer parts. The main result of this paper is a justification of an asymptotic expansion for the solutions of this Cauchy problem. Our method can be applied in a wide variety of cases for singularly perturbed Cauchy problems of Fokker-Planck equations.
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Rogacheva, Nelly. "THE REFINED THEORY OF ELASTIC PLATES AS ASYMPTOTIC APPROACH OF 3D PROBLEM." MATEC Web of Conferences 196 (2018): 02037. http://dx.doi.org/10.1051/matecconf/201819602037.

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The refined theory of elastic thin and thick plates is constructed by the asymptotic method for reducing three-dimensional (3D) equations of linear elasticity to two-dimensional ones without the use of any assumptions. The resulting refined theory is much more complicated than the known classical Kirchhoff theory: the required values of the refined theory vary in thickness of the plate by more complex laws; the system of partial differential equations of the refined theory has a higher order than the system of equations of the classical theory. A comparison of the obtained theory with the popular refined theory of Timoshenko and E. Reissner, taking into account the transverse shear deformation is made. It is shown that the inclusion only of the transverse shear deformation is insufficient. In addition to the transverse shear deformation, many additional terms having the same order as the transverse shear deformation must be taken into account.
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Hayashi, Nakao, and Elena I. Kaikina. "Benjamin-Ono Equation on a Half-Line." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–38. http://dx.doi.org/10.1155/2010/714534.

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We consider the initial-boundary value problem for Benjamin-Ono equation on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.
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Hibino, Masaki. "Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type — Part I —." Communications on Pure & Applied Analysis 2, no. 2 (2003): 211–31. http://dx.doi.org/10.3934/cpaa.2003.2.211.

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Allognissode, Fulbert Kuessi, Mamadou Abdoul Diop, Khalil Ezzinbi, and Carlos Ogouyandjou. "Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior." Random Operators and Stochastic Equations 27, no. 2 (June 1, 2019): 107–22. http://dx.doi.org/10.1515/rose-2019-2009.

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Abstract This paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion {S_{Q}^{H}(t)} , with Hurst parameter {H\in(\frac{1}{2},1)} . By the theory of resolvent operator developed by R. Grimmer (1982) to establish the existence of mild solutions, we give sufficient conditions ensuring the existence, uniqueness and the asymptotic behavior of the mild solutions. An example is provided to illustrate the theory.
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Dissertations / Theses on the topic "Differential equations, Partial – Asymptotic theory"

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Coats, J. "High frequency asymptotics of antenna/structure interactions." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249595.

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This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors. We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point. In chapter 5 we review and extend the asymptotic results concerning illumination of a convex perfect conductor by an incident plane wave and outline the procedure for decoupling the electromagnetic surface field into two scalar modes. In chapter 6 we place a source on a perfect conductor and obtain a complete asymptotic solution for the fields. Special attention is paid to the asymptotic structure that smoothly matches between the leading order lit and shadow regions. We also investigate the degenerate case where one of the curvatures of the perfect conductor is zero. The case where the source is just off the surface is also investigated. In chapter 8 we use the Euler-Maclaurin summation formula to cheaply calculate the fields due to complicated arrays of point dipoles. The final chapter combines many earlier results to consider more general sources on the surface of a perfect conductor. In particular we must introduce new asymptotic regions for open sources. This then enables us to consider the focussing of the surface field due to a finite source. The nature of the surface and geometrical optics fields depends on the size of the source in comparison to the curvatures of the surface on which they lie. We discuss this in detail and conclude with the practical example of a spiral antenna.
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Coimbra, Tiago Antonio Alves 1981. "Operação para continuação do afastamento : operador diferencial, comportamento dinâmico e empilhamento multi-paramétrico." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306033.

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Orientadores: Maria Amélia Novais Schleicher, Joerg Dietrich Wilhelm Schleicher
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-24T12:48:22Z (GMT). No. of bitstreams: 1 Coimbra_TiagoAntonioAlves_D.pdf: 11322080 bytes, checksum: 57d63d91892a162c542c0a1d25e3c08b (MD5) Previous issue date: 2014
Resumo: A operação para continuação de afastamento (Offset Continuation Operation - OCO) transforma um registro sísmico adquirido com um certo afastamento entre fonte e receptor, em um registro correspondente como se fosse adquirido com outro afastamento. O deslocamento de um evento sísmico sob esta operação pode ser descrito por uma equação diferencial parcial de segunda ordem. Baseado na aproximação WKBJ, deduzimos uma equação tipo iconal OCO que descreve os aspectos cinemáticos deste deslocamento em analogia a uma onda acústica, e uma equação de transporte que descreve a alteração das amplitudes. Baseado na teoria dos raios representamos uma forma de solução para a nova equação proposta. Notamos que operadores diferencias de transformação de configuração que corrigem o fator de espalhamento geométrico para qualquer afastamento, ao menos de modo assintótico, são novos na literatura. Baseados na cinemática da operação, propomos um operador de empilhamento multi-paramétrico no domínio não-migrado dos dados sísmicos. Esse empilhamento multi-paramétrico usa uma velocidade média, chamada de velocidade OCO, bem como outros parâmetros cinemáticos do campo de onda importantes. Por se basear na OCO, os tempos de trânsito usados neste empilhamento multi-paramétrico acompanham a trajetória OCO que aproxima à verdadeira trajetória do ponto de reflexão comum. Assim, os parâmetros extraídos servem para melhorar a correção do sobretempo convencional ou realizar correções correspondentes para afastamentos não nulos. Desta forma, é possível aumentar a qualidade das seções empilhadas convencionais de afastamento nulo ou até gerar seções empilhadas de outros afastamentos. Os parâmetros cinemáticos envolvidos ainda podem ser utilizado para construir um melhor modelo de velocidade. Exemplos numéricos mostram que o empilhamento usando trajetórias OCO aumenta, de forma significativa, a qualidade dos dados com uso de menos parâmetros que nos métodos clássicos
Abstract: The Offset Continuation Operation (OCO) transforms a seismic record with a certain offset between source and receiver in another record as if obtained with another offset. The displacement between a seismic event under this operation may be modeled by a second order partial differential equation. We base on the WKBJ approximation and deduce an OCO equation type-eikonal and a transport equation. The former decribes the kinematic features of this displacement, analogously to an acoustic wave, and the latter describes the change of the amplitudes. We present a solution for the proposed new equation, based on the ray theory. The differential configuration transformation operators that correct the geometric spreading for any common offset section (CO) in an asymptoptic way are a novelty in the literature. Based on the kinematics of the operation, we propose a multi-parametric stacking on the unmigrated data domain. This multi-parametric use stacking average velocity called OCO velocity and other kinematic parameters important field from waveform. Since it is based on OCO, travel times used in this multi-parametric stacking accompany OCO trajectory that approximates the true trajectory of the common reflection point (CRP). Thus, the extracted parameters are used to improve the precision of the moveout or to do corresponding corrections for nonzero offsets. Thus, it is possible to increase the quality of conventional sections stacked in zero offset or even generate stacked sections other common offsets. The kinematic parameters involved can also be used to build a velocity model better. Numerical examples show that the stacking using trajectories OCO increases, significantly, the quality of the data using fewer parameters than the classical methods
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Kasonga, Raphael Abel Carleton University Dissertation Mathematics. "Asymptotic parameter estimation theory for stochastic differential equations." Ottawa, 1986.

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Jenab, Bita. "Asymptotic theory of second-order nonlinear ordinary differential equations." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24690.

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The asymptotic behaviour of nonoscillatory solutions of second order nonlinear ordinary differential equations is studied. Necessary and sufficient conditions are given for the existence of positive solutions with specified asymptotic behaviour at infinity. Existence of nonoscillatory solutions is established using the Schauder-Tychonoff fixed point theorem. Techniques such as factorization of linear disconjugate operators are employed to reveal the similar nature of asymptotic solutions of nonlinear differential equations to that of linear equations. Some examples illustrating the asymptotic theory of ordinary differential equations are given.
Science, Faculty of
Mathematics, Department of
Graduate
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Chulkov, Sergei. "Topics in analytic theory of partial differential equations /." Stockholm : Dept. of mathematics, Stockholm university, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-782.

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Huang, Guan. "An averaging theory for nonlinear partial differential equations." Palaiseau, Ecole polytechnique, 2014. http://pastel.archives-ouvertes.fr/docs/01/00/25/27/PDF/these.pdf.

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Cette thèse se consacre aux études des comportements de longtemps des solutions pour les EDPs nonlinéaires qui sont proches d'une EDP linéaire ou intégrable hamiltonienne. Une théorie de la moyenne pour les EDPs nonlinéaires est presenté. Les modèles d'équations sont les équations Korteweg-de Vries (KdV) perturbées et quelques équations aux dérivées partielles nonlinéaires faiblement
This Ph. D thesis focuses on studying the long-time behavior of solutions for non-linear PDEs that are close to a linear or an integrable Hamiltonian PDE. An averaging theory for nonlinear PDEs is presented. The model equations are the perturbed Korteweg-de Vries (KdV) equations and some weakly nonlinear partial differential equations
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Mateos, González Álvaro. "Asymptotic Analysis of Partial Differential Equations Arising in Biological Processes of Anomalous Diffusion." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN069/document.

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Cette thèse est consacrée à l'analyse asymptotique d'équations aux dérivées partielles issues de modèles de déplacement sous-diffusif en biologie cellulaire. Notre motivation biologique est fondée sur les nombreuses observation récentes de protéinescytoplasmiques dont le déplacement aléatoire dévié de la diffusion Fickienne normale. Dans la première partie, nous étudions la décroissance auto-similaire de la solution d'une équation de renouvellement à queue lourde vers un état stationnaire. Les idéesmises en jeu sont inspirées de méthodes d'entropie relative. Nos principaux apports sont la preuve d'un taux de décroissance en norme L1 vers la loi de l'arc-sinus et l'introduction d'une fonction pivot spécifique dans une méthode d'entropie relative.La seconde partie porte sur la limite hyperbolique d'une équation de renouvellement structurée en âge et à sauts en espace. Nous y prouvons un résultat de « stabilité » : les solutions des problèmes rééchelonnés à ε > 0 convergent lorsque ε --> 0 vers la solution de viscosité de l'équation de Hamilton-Jacobi limite des problèmes à ε > 0. Les outilsmis en jeu proviennent de la théorie des équations de Hamilton-Jacobi.Ce travail présente trois idées intéressantes. La première est celle de prouver le résultat de convergence sur la condition de bord du problème plutôt que d'utiliser des fonctions test perturbées. La deuxième consiste en l'introduction de termes correcteurslogarithmiques en temps dans des estimations a priori ne découlant pas directementdu principe du maximum. Cela est dû à la non-existence d'un équilibre du problèmehomogène en espace. La troisième est une estimation précise de la décroissance de l'influence de la condition initiale sur le terme de renouvellement. Elle correspond à une estimation fine d'une version non-locale de la dérivée temporelle de la solution. Au cours de cette thèse, des simulations numériques de type Monte Carlo, schémas volumes finis, Lax-Friedrichs et Weighted Essentially Non Oscillating ont été réalisées
This thesis is devoted to the asymptotic analysis of partial differential equations modelling subdiffusive random motion in cell biology. The biological motivation for this work is the numerous recent observations of cytoplasmic proteins whose random motion deviates from normal Fickian diffusion. In the first part, we study the self-similar decay towards a steady state of the solution of a heavy-tailed renewal equation. The ideas therein are inspired from relative entropy methods. Our main contributions are the proof of an L1 decay rate towards the arc-sine distribution and the introduction of a specific pivot function in a relative entropy method.The second part treats the hyperbolic limit of an age-structured space-jump renewal equation. We prove a "stability" result: the solutions of the rescaled problems at ε > 0 converge as ε --> 0 towards the viscosity solution of the limiting Hamilton-Jacobi equation of the ε > 0 problems. The main mathematical tools used come from the theory of Hamilton-Jacobi equations. This work presents three interesting ideas. The first is that of proving the convergence result on the boundary condition of the studied problem rather than using perturbed test functions. The second consists in the introduction of time-logarithmic correction termsin a priori estimates that do not follow directly from the maximum principle. That is due to the non-existence of a suitable equilibrium for the space-homogenous problem. The third is a precise estimate of the decay of the inuence of the initial condition on the renewal term. This is tantamount to a refined estimate of a non-local version of the time derivative of the solution. Throughout this thesis, we have performed numerical simulations of different types: Monte Carlo, finite volume schemes, Lax-Friedrichs schemes and Weighted Essentially Non Oscillating schemes
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Howard, Timothy G. "Predicting the asymptotic behavior for differential equations with a quadratic nonlinearity." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/28823.

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Shi, Changgui. "The global behavior of solutions of a certain third order differential equation." Virtual Press, 1992. http://liblink.bsu.edu/uhtbin/catkey/834515.

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In computer vision, object recognition involves segmentation of the image into separate components. One way to do this is to detect the edges of the components. Several algorithms for edge detection exist and one of the most sophisticated is the Canny edge detector.Canny [2] designed an optimal edge detector for images which are corrupted with noise. He suggested that a Gaussian filter be applied to the image and edges be sought in the smoothed image. The directional derivative of the Gaussian is obtained, then convolved with the image. The direction, n, involved is normal to the edge direction. Edges are assumed to exist where the result is a local extreme, i.e., where∂2 (g * f) = 0.(0.1)_____∂n2In the above, g(x, y) is the Gaussian, f (x, y) is the image function and The direction of n is an estimate of the direction of the gradient of the true edge. In this thesis, we discuss the computational algorithm of the Canny edge detector and its implementation. Our experimental results show that the Canny edge detection scheme is robust enough to perform well over a wide range of signal-to-noise ratios. In most cases the Canny edge detector performs much better than the other edge detectors.
Department of Mathematical Sciences
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Lattimer, Timothy Richard Bislig. "Singular partial integro-differential equations arising in thin aerofoil theory." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243192.

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Books on the topic "Differential equations, Partial – Asymptotic theory"

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Bouchut, François. Kinetic equations and asymptotic theory. Paris: Gauthier-Villars, 2000.

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Some asymptotic problems in the theory of partial differential equations. Cambridge: Cambridge University Press, 1996.

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Hale, Jack K. Asymptotic behavior of dissipative systems. Providence, R.I: American Mathematical Society, 1988.

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Vladimir, Kozlov. Asymptotic analysis of fields in multi-structures. Oxford: Oxford University Press, 1999.

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NATO Advanced Workshop on Asymptotic-Induced Numerical Methods for Partial Differential Equations, Critical Parameters, and Domain Decomposition (1992 Beaune, France). Asymptotic and numerical methods for partial differential equations with critical parameters. Edited by Kaper H. G and Garbey Marc 1955-. Dordrecht: Kluwer Academic, 1993.

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Rao, Ch. Srinivasa (Chidella Srinivasa), ed. Large time asymptotics for solutions of nonlinear partial differential equations. New York: Springer, 2010.

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Reissig, Michael. Progress in Partial Differential Equations: Asymptotic Profiles, Regularity and Well-Posedness. Heidelberg: Springer International Publishing, 2013.

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Mazʹi︠a︡, V. G. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Basel: Birkhäuser Verlag, 2000.

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Asymptotic analysis of soliton problems: An inverse scattering approach. Berlin: Springer-Verlag, 1986.

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Amrein, Werner O. Hardy type inequalities for abstract differential operators. Providence, R.I., USA: American Mathematical Society, 1987.

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Book chapters on the topic "Differential equations, Partial – Asymptotic theory"

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Lim, S. C., and S. V. Muniandy. "Local Asymptotic Properties of Multifractional Brownian Motion." In Partial Differential Equations and Spectral Theory, 205–14. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_23.

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Denk, Robert, and Leonid Volevich. "Parameter-Elliptic Boundary Value Problems and their Formal Asymptotic Solutions." In Partial Differential Equations and Spectral Theory, 103–11. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_12.

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Seiringer, Robert. "Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula." In Partial Differential Equations and Spectral Theory, 307–14. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_35.

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Witt, Ingo. "Cone Conormal Asymptotics." In Partial Differential Equations and Spectral Theory, 329–36. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_38.

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Brauner, Claude-Michel, Lina Hu, and Luca Lorenzi. "Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation." In Partial Differential Equations: Theory, Control and Approximation, 139–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-41401-5_5.

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de Monvel, L. Boutet. "Toeplitz Operators and Asymptotic Equivariant Index." In Modern Aspects of the Theory of Partial Differential Equations, 1–16. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0069-3_1.

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Bruneau, Vincent, and Vesselin Petkov. "Semi-Classical Resolvent Estimates and Spectral Asymptotics for Trapping Perturbations." In Partial Differential Equations and Spectral Theory, 37–40. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_5.

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Pignotti, Cristina, and Irene Reche Vallejo. "Asymptotic Analysis of a Cucker–Smale System with Leadership and Distributed Delay." In Trends in Control Theory and Partial Differential Equations, 233–53. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17949-6_12.

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Siedentop, Heinz. "A statistical theory of heavy atoms: Asymptotic behavior of the energy and stability of matter." In Partial Differential Equations, Spectral Theory, and Mathematical Physics, 389–403. Zuerich, Switzerland: European Mathematical Society Publishing House, 2021. http://dx.doi.org/10.4171/ecr/18-1/23.

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Reissig, Michael. "Optimality of the Asymptotic Behavior of the Energy for Wave Models." In Modern Aspects of the Theory of Partial Differential Equations, 291–315. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0069-3_17.

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Conference papers on the topic "Differential equations, Partial – Asymptotic theory"

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MIYAKE, MASATAKE, and KUNIO ICHINOBE. "HIERARCHY OF PARTIAL DIFFERENTIAL EQUATIONS AND FUNDAMENTAL SOLUTIONS ASSOCIATED WITH SUMMABLE FORMAL SOLUTIONS OF A PARTIAL DIFFERENTIAL EQUATION OF NON KOWALEVSKI TYPE." In Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0009.

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TAHARA, HIDETOSHI. "ON THE SINGULARITIES OF SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN, II." In Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0010.

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Guo, Xiang-Ying, Wei Zhang, and Qian Wang. "Nonlinear Vibration Response Analysis on a Composite Plate Reinforced With Carbon Nanotubes." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85856.

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In order to compare nonlinear vibration response of the different enabled materials in the matrix of composites, the nonlinear vibrations of a composite plate reinforced with carbon nanotubes (CNT) are studied. In this paper, the carbon nanotubes are supposed to be long fibers. The nonlinear governing partial differential equations of motion for the composite rectangular thin plate are derived by using the Reddy’s third-order shear deformation plate theory, the von Karman type equation and the Hamilton’s principle. Then, the governing equations get reduced to ordinary differential equations in thickness direction with variable coefficients and these are solved by the Galerkin method. The case of 1:1 internal resonance is considered. The asymptotic perturbation method is employed to obtain the four-dimensional averaged equations. The numerical method is used to investigate the periodic and chaotic motions of the composite rectangular thin plate reinforced with carbon nanotubes. The results of numerical simulation demonstrate that there exist different kinds of periodic and chaotic motions of the composite plate under certain conditions. At last, the nonlinear vibration responses of the plate are compared with the same responses of angle-ply composite laminated plates.
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Zhang, Yuhong, and Sunil Agrawal. "A Lyapunov Controller for a Varying Length Flexible Cable System to Supress Transverse Vibration." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60269.

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Modeling and controller design for a flexible cable transporter system, with arbitrarily varying cable length is presented using Hamilton’s principle and Lyapunov theory. The axial velocity of the system is assumed to be arbitrary in the model. This is different from existing literature where the axial velocity is assumed either constant or is prescribed. The governing equations are coupled non-linear partial differential equations (PDEs) and ordinary differential equations (ODEs), and boundary conditions. The interactions between the cables and the slider, pulleys, and motors are included in the model. Numerical solution of the governing equations is obtained using Galerkin’s method. Based on the Lyapunov stability theory, we propose boundary controllers and the control law for an actuator within the domain to suppress the transverse vibration of the cables, while achieving the slider goal. The proposed controllers dissipate the vibratory energy and guarantee asymptotic stability of the closed-loop system. Simulation results demonstrate the effectiveness of the proposed controllers.
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Liu, Shuyang, Reza Langari, and Yuanchun Li. "Control Design for the System of Manipulator Handling a Flexible Payload With Input Constraints." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-8970.

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In this paper, we consider the control design for manipulator handling a flexible payload in the presence of input constraints. The dynamics of the system is described by coupled ordinary differential equation and a partial differential equation. Considering actuators saturation, the proposed control law applies a smooth hyperbolic function to handle the effect of the input constraints. The asymptotic stability of the closed-loop system is proved by using semigroup theory and extended LaSalle’s Invariance Principle. Simulation results show that the proposed controller is effective.
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King, Melvin E., and Alexander F. Vakakis. "Nonlinear Normal Modes in a Class of Nonlinear Continuous Systems." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0030.

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Abstract A general methodology is developed for computing the nonlinear normal modes of a class of undamped vibratory systems governed by nonlinear partial differential equations of motion. A nonlinear normal mode is defined as free motion during which all points of the system vibrate equiperiodically, reaching their extremum positions at the same instants of time. The analytical methodology is based on a previous work by Shaw and Pierre (1992b), where the displacements and velocities at any point of a structure were expressed as functions of the displacement and velocity of a single reference point. The dynamics of the continuous system were then restricted to invariant manifolds of the phase space. Motivated by the methodology presented by Shaw and Pierre, we express the displacement of an arbitrary point of the structure as a function of the displacement of a single reference point. Assuming undamped oscillations (and thus conservation of energy), a singular partial differential equation for the function relating the displacements is derived, and is subsequently solved using an asymptotic, power series methodology. Applications of the general theory are then given by computing the nonlinear normal modes of a simply supported beam resting on a nonlinear elastic foundation, and of a cantilever beam having geometric nonlinearities. The stability of the detected modes is then investigated by a linearized stability analysis.
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Lee, Ho-Hoon. "Modeling and Control of a Horizontal Two-Link Rigid/Flexible Robot." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81730.

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This paper proposes a trajectory control scheme for a horizontal two-link rigid/flexible robot having a payload at the free end. First, a new distributed-parameter dynamic model, consisting of two ordinary differential equations and one partial differential equation, is derived using the extended Hamilton’s principle, and then a trajectory-tracking control scheme is designed based on the distributed-parameter dynamic model, where the Lyapunov stability theorem is used as a mathematical tool. The proposed control is a collocated control, free from the so-called spillover instability. The proposed control consists of a PD control for the rigid dynamics, a proportional control for the flexible dynamics, and feed forward and dynamics compensation. With only two joint actuators, the proposed trajectory control guarantees stability throughout the entire trajectory-tracking control and asymptotic stability at desired goal positions. The theoretical results have been evaluated with control experiments.
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Zhang, Wei, Ming-Hui Yao, and Dong-Xing Cao. "Shilnikov Type Multi-Pulse Orbits of Functionally Graded Materials Rectangular Plate." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29206.

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Multi-pulse chaotic dynamics of a simply supported functionally graded materials (FGMs) rectangular plate is investigated in this paper. The FGMs rectangular plate is subjected to the transversal and in-plane excitations. The properties of material are graded in the direction of thickness. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the FGMs plate are derived by using the Hamilton’s principle. The four-dimensional averaged equation under the case of 1:2 internal resonance, primary parametric resonance and 1/2-subharmonic resonance is obtained by directly using the asymptotic perturbation method and Galerkin approach to the partial differential governing equation of motion for the FGMs rectangular plate. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the FGMs rectangular plate. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the FGMs rectangular plate are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported FGMs rectangular plate.
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Vakakis, A. F., and M. E. King. "A Nonlinear Normal Mode Approach for Studying Waves in Nonlinear Monocoupled Periodic Systems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0324.

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Abstract The free dynamics of a mono-coupled layered nonlinear periodic system of infinite extent is analyzed. It is shown that, in analogy to linear theory, the system possesses nonlinear attenuation and propagation zones (AZs and PZs) in the frequency domain. Responses in AZs correspond to standing waves with spatially attenuating, or expanding envelopes, and are synchronous motions of all points of the periodic system. These motions are analytically examined by employing the notion of “nonlinear normal mode,” thereby reducing the response problem to the solution of an infinite set of singular nonlinear partial differential equations. An asymptotic methodology is developed to solve this set. Numerical computations are carried out to complement the analytical findings. The methodology developed in this work can be extended to investigate synchronous attenuating motions of multi-coupled nonlinear periodic systems.
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WONG, RODERICK S. C. "FIVE LECTURES ON ASYMPTOTIC THEORY." In Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0004.

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Reports on the topic "Differential equations, Partial – Asymptotic theory"

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Dresner, L. Asymptotic behavior of solutions of diffusion-like partial differential equations invariant to a family of affine groups. Office of Scientific and Technical Information (OSTI), July 1990. http://dx.doi.org/10.2172/6697591.

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