Relevant bibliographies by topics / Operator equations, Nonlinear

Contents

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

Academic literature on the topic 'Operator equations, Nonlinear'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Operator equations, Nonlinear"

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Burýšková, Věra, and Slavomír Burýšek. "On solvability of nonlinear operator equations and eigenvalues of homogeneous operators." Mathematica Bohemica 121, no. 3 (1996): 301–14. http://dx.doi.org/10.21136/mb.1996.125984.

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Takači, Djurdjica. "Nonlinear operator differential equations." Nonlinear Analysis: Theory, Methods & Applications 30, no. 1 (December 1997): 47–52. http://dx.doi.org/10.1016/s0362-546x(97)00404-5.

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Ryazantseva, Irina P. "Simplification method for nonlinear equations of monotone type in Banach space." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 2 (June 30, 2021): 185–92. http://dx.doi.org/10.15507/2079-6900.23.202102.185-192.

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Abstract. In a Banach space, we study an operator equation with a monotone operator T. The operator is an operator from a Banach space to its conjugate, and T=AC, where A and C are operators of some classes. The considered problem belongs to the class of ill-posed problems. For this reason, an operator regularization method is proposed to solve it. This method is constructed using not the operator T of the original equation, but a more simple operator A, which is B-monotone, B=C−1. The existence of the operator B is assumed. In addition, when constructing the operator regularization method, we use a dual mapping with some gauge function. In this case, the operators of the equation and the right-hand side of the given equation are assumed to be perturbed. The requirements on the geometry of the Banach space and on the agreement conditions for the perturbation levels of the data and of the regularization parameter are established, which provide a strong convergence of the constructed approximations to some solution of the original equation. An example of a problem in Lebesgue space is given for which the proposed method is applicable.
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Binh, Tran Quoc, and Nguyen Minh Chuong. "APPROXIMATION OF NONLINEAR OPERATOR EQUATIONS*." Numerical Functional Analysis and Optimization 22, no. 7-8 (November 30, 2001): 831–44. http://dx.doi.org/10.1081/nfa-100108311.

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Marchenko, V. A. "Nonlinear equations and operator algebras." Physica D: Nonlinear Phenomena 28, no. 1-2 (September 1987): 227. http://dx.doi.org/10.1016/0167-2789(87)90152-7.

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Motsa, S. S. "On the Optimal Auxiliary Linear Operator for the Spectral Homotopy Analysis Method Solution of Nonlinear Ordinary Differential Equations." Mathematical Problems in Engineering 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/697845.

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The purpose of this study is to identify the auxiliary linear operator that gives the best convergence and accuracy in the implementation of the spectral homotopy analysis method (SHAM) in the solution of nonlinear ordinary differential equations. The auxiliary linear operator is an essential element of the homotopy analysis method (HAM) algorithm that strongly influences the convergence of the method. In this work we introduce new procedures of defining the auxiliary linear operators and compare solutions generated using the new linear operators with solutions obtained using well-known linear operators. The applicability and validity of the proposed linear operators is tested on four highly nonlinear ordinary differential equations with fluid mechanics applications that have recently been reported in the literature. The results from the study reveal that the new linear operators give better results than the previously used linear operators. The identification of the optimal linear operator will direct future research on further applications of HAM-based methods in solving complicated nonlinear differential equations.
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Argyros, Ioannis K., Santhosh George, and P. Jidesh. "Inverse Free Iterative Methods for Nonlinear Ill-Posed Operator Equations." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/754154.

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We present a new iterative method which does not involve inversion of the operators for obtaining an approximate solution for the nonlinear ill-posed operator equationF(x)=y. The proposed method is a modified form of Tikhonov gradient (TIGRA) method considered by Ramlau (2003). The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005). The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper.
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Hofmann, Bernd, and Robert Plato. "On ill-posedness concepts, stable solvability and saturation." Journal of Inverse and Ill-posed Problems 26, no. 2 (April 1, 2018): 287–97. http://dx.doi.org/10.1515/jiip-2017-0090.

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AbstractWe consider different concepts of well-posedness and ill-posedness and their relations for solving nonlinear and linear operator equations in Hilbert spaces. First, the concepts of Hadamard and Nashed are recalled which are appropriate for linear operator equations. For nonlinear operator equations, stable respective unstable solvability is considered, and the properties of local well-posedness and ill-posedness are investigated. Those two concepts consider stability in image space and solution space, respectively, and both seem to be appropriate concepts for nonlinear operators which are not onto and/or not, locally or globally, injective. Several example situations for nonlinear problems are considered, including the prominent autoconvolution problems and other quadratic equations in Hilbert spaces. It turns out that for linear operator equations, well-posedness and ill-posedness are global properties valid for all possible solutions, respectively. The special role of the nullspace is pointed out in this case. Finally, non-injectivity also causes differences in the saturation behavior of Tikhonov and Lavrentiev regularization of linear ill-posed equations. This is examined at the end of this study.
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Çavuş, Abdullah, Djavvat Khadjiev, and Seda Öztürk. "On periodic solutions to nonlinear differential equations in Banach spaces." Filomat 30, no. 4 (2016): 1069–76. http://dx.doi.org/10.2298/fil1604069c.

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Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complex Banach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator and denoted by R? is defined for points of the spectrum, some equivalent conditions for compactness of the quasi-resolvent operators R? are given. Then using these, some theorems on existence of periodic solutions to the non-linear equations ?(A)x = f (x) are given, where ?(A) is a polynomial of A with complex coefficients and f is a continuous mapping of H into itself.
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ARAI, ASAO. "HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION." Reviews in Mathematical Physics 19, no. 10 (November 2007): 1045–69. http://dx.doi.org/10.1142/s0129055x07003206.

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An abstract operator theory is developed on operators of the form AH(t) := eitHAe-itH, t ∈ ℝ, with H a self-adjoint operator and A a linear operator on a Hilbert space (in the context of quantum mechanics, AH(t) is called the Heisenberg operator of A with respect to H). The following aspects are discussed: (i) integral equations for AH(t) for a general class of A; (ii) a sufficient condition for D(A), the domain of A, to be left invariant by e-itH for all t ∈ ℝ; (iii) a mathematically rigorous formulation of the Heisenberg equation of motion in quantum mechanics and the uniqueness of its solutions; (iv) invariant domains in the case where H is an abstract version of Schrödinger and Dirac operators; (v) applications to Schrödinger operators with matrix-valued potentials and Dirac operators.
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Dissertations / Theses on the topic "Operator equations, Nonlinear"

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Pudipeddi, Sridevi Iaia Joseph A. "Localized radial solutions for nonlinear p-laplacian equation in R[superscript N]." [Denton, Tex.] : University of North Texas, 2008. http://digital.library.unt.edu/permalink/meta-dc-6059.

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Adhikari, Dhruba R. "Applications of degree theories to nonlinear operator equations in Banach spaces." [Tampa, Fla.] : University of South Florida, 2007. http://purl.fcla.edu/usf/dc/et/SFE0002158.

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Pudipeddi, Sridevi. "Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN." Thesis, University of North Texas, 2008. https://digital.library.unt.edu/ark:/67531/metadc6059/.

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We establish the existence of radial solutions to the p-Laplacian equation ∆p u + f(u)=0 in RN, where f behaves like |u|q-1 u when u is large and f(u) < 0 for small positive u. We show that for each nonnegative integer n, there is a localized solution u which has exactly n zeros. Also, we look for radial solutions of a superlinear Dirichlet problem in a ball. We show that for each nonnegative integer n, there is a solution u which has exactly n zeros. Here we give an alternate proof to that which was given by Castro and Kurepa.
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Abdeljabbar, Alrazi. "Wronskian, Grammian and Pfaffian Solutions to Nonlinear Partial Differential Equations." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/3939.

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It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also variable coefficients under a certain constraint (ut + α 1(t)uxxy + 3α 2(t)uxuy)x +α 3 (t)uty -α 4(t)uzz + α 5(t)(ux + α 3(t)uy) = 0. However, bilinear equations are the nearest neighbors to linear equations, and expected to have some properties similar to those of linear equations. We have explored a key feature of the linear superposition principle, which linear differential equations have, for Hirota bilinear equations, while intending to construct a particular sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are given for the (3+1) dimensional KP, Jimbo-Miwa (JM) and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is also raised and discussed about generating Hirota bilinear equations possessing the indicated N-wave solutions, and two illustrative examples are presented. Using the Pfaffianization procedure, we have extended the generalized KP equation to a generalized KP system of nonlinear PDEs. Wronskian-type Pfaffian and Gramm-type Pfaffian solutions of the resulting Pfaffianized system have been presented. Our results and computations basically depend on Pfaffian identities given by Hirota and Ohta. The Pl̈ucker relation and the Jaccobi identity for determinants have also been employed. A (3+1)-dimensional JM equation has been considered as another important example in soliton theory, uyt - uxxxy - 3(uxuy)x + 3uxz = 0. Three kinds of exact soliton solutions have been given: Wronskian, Grammian and Pfaffian solutions. The Pfaffianization procedure has been used to extend this equation as well. Within Wronskian and Pfaffian formulations, soliton solutions and rational solutions are usually expressed as some kind of logarithmic derivatives of Wronskian and Pfaffian type determinants and the determinants involved are made of functions satisfying linear systems of differential equations. This connection between nonlinear problems and linear ones utilizes linear theories in solving soliton equations. B̈acklund transformations are another powerful approach to exact solutions of nonlinear equations. We have computed different classes of solutions for a (3+1)-dimensional generalized KP equation based on a bilinear B̈acklund transformation consisting of six bilinear equations and containing nine free parameters. A variable coefficient Boussinesq (vcB) model in the long gravity water waves is one of the examples that we are investigating, ut + α 1 (t)uxy + α 2(t)(uw)x + α 3(t)vx = 0; vt + β1(t)(wvx + 2vuy + uvy) + β2(t)(uxwy - (uy)2) + β3(t)vxy + β4(t)uxyy = 0, where wx = uy. Double Wronskian type solutions have been constructed for this (2+1)-dimensional vcB model.
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Ali, Jaffar. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Diss., Mississippi State : Mississippi State University, 2008. http://library.msstate.edu/etd/show.asp?etd=etd-07082008-153843.

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Asaad, Magdy. "Pfaffian and Wronskian solutions to generalized integrable nonlinear partial differential equations." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/3956.

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The aim of this work is to use the Pfaffian technique, along with the Hirota bilinear method to construct different classes of exact solutions to various of generalized integrable nonlinear partial differential equations. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions. The derivation and solutions of integrable nonlinear partial differential equations in two spatial dimensions have been the holy grail in the field of nonlinear science since the late 1960s. The prestigious Korteweg-de Vries (KdV) and nonlinear Schrödinger (NLS) equations, as well as the ,Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable nonlinear partial differential equations in (1+1) and (2+1) dimensions, respectively. Do there exist Pfaffian and soliton solutions to generalized integrable nonlinear partial differential equations in (3+1) dimensions? In this dissertation, I obtained a set of explicit exact Wronskian, Grammian, Pfaffian and N-soliton solutions to the (3+1)-dimensional generalized integrable nonlinear partial differential equations, including a generalized KP equation, a generalized B-type KP equation, a generalized modified B-type KP equation, soliton equations of Jimbo-Miwa type, the nonlinear Ma-Fan equation, and the Jimbo-Miwa equation. A set of sufficient conditions consisting of systems of linear partial differential equations involving free parameters and continuous functions is generated to guarantee that the Wronskian determinant or the Pfaffian solves these generalized equations. On the other hand, as part of this dissertation, bilinear Bäcklund transformations are formally derived for the (3+1)-dimensional generalized integrable nonlinear partial differential equations: a generalized B-type KP equation, the nonlinear Ma-Fan equation, and the Jimbo-Miwa equation. As an application of the obtained Bäcklund transformations, a few classes of traveling wave solutions, rational solutions and Pfaffian solutions to the corresponding equations are explicitly computed. Also, as part of this dissertation, I would like to apply the Pfaffianization mechanism of Hirota and Ohta to extend the (3+1)-dimensional variable-coefficient soliton equation of Jimbo-Miwa type to coupled systems of nonlinear soliton equations, called Pfaffianized systems. Examples of the Wronskian, Grammian, Pfaffian and soliton solutions are explicitly computed. The numerical simulations of the obtained solutions are illustrated and plotted for different parameters involved in the solutions.
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López, Ríos Luis Fernando. "Two problems in nonlinear PDEs : existence in supercritical elliptic equations and symmetry for a hypo-elliptic operator." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/115530.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática
En este trabajo se aborda el problema de encontrar soluciones regulares para algunas EDPs elípticas e hipo-elípticas no lineales y estudiar sus propiedades cualitativas. En una primera etapa, se considera la ecuación $$ -\Delta u = \lambda e^u, $$ $\lambda > 0$, en un dominio exterior con condición de Dirichlet nula. Un esquema de reducción finito-dimensional permite encontrar infinitas soluciones regulares cuando $\lambda$ es suficientemente pequeño. En la segunda parte se estudia la existencia de soluciones de la ecuación no local $$ (-\Delta)^s u = u^{p \pm \epsilon}, u > 0, $$ en un dominio acotado y suave, con condición de Dirichlet nula; donde $s > 0$ y $p:=(N+2s)/(N-2s) \pm \epsilon$ es cercano al exponente crítico ($\epsilon > 0$ pequeño). Para hallar soluciones, se utiliza un esquema de reducción finito-dimensional en espacios de funciones adecuados, donde el término principal de la función reducida se expresa a partir de las funciones de Green y de Robin del dominio. La existencia de soluciones dependerá de la existencia de puntos críticos de este término principal y de una condición de no degeneración. Por último, se considera un problema no local en el grupo de Heisenberg $H$. En particular, se buscan propiedades de rigidez para soluciones estables de $$ (-\Delta_H)^s v = f(v) en H, $$ $s \in (0,1)$. Como paso fundamental, se prueba una desigualdad del tipo Poincaré en conexión con un problema elíptico degenerado en $R^4_+$. Esta desigualdad se usará en un procedimiento de extensión para dar un criterio bajo el cual los conjuntos de nivel de las soluciones del problema anterior son superficies mínimas en $H$, es decir, tienen $H$-curvatura media nula.
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Lopez, Rios Luis Fernando. "Two problems in nonlinear PDEs : existence in supercritical elliptic equations and symmetry for a hypo-elliptic operator." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4701/document.

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Le travail présenté est dédié à des problèmes d'EDP non linéaires. L'idée principale est de construire des solutions régulières á certaines EDPs elliptiques et hypo-elliptiques et étudier leur propriétés qualitatives. Dans une première partie, on considère un problème sur-critique du type $$-Delta u = lambda e^u$$ avec $lambda > 0$ posé dans un domaine extérieur avec conditions de Dirichlet homogènes. Une réduction en dimension finie permet de prouver l'existence d'un nombre infini de solutions régulières quand $lambda$ est assez petit. Dans une deuxième partie, on étudie la concentration de solutions d'un problème non local $$(-Delta)^s u = u^{p pm epsilon}, u>0, epsilon > 0$$ dans un domaine borné, régulier sous conditions de Dirichlet homogènes. Ici, on prend $0 < s < 1$ et $p:=(N+2s)/(N-2s)$, l'exposant de Sobolev critique. Une réduction en dimension finie dans des espaces fonctionnels bien choisis est utilisée. La partie principale de la fonction réduite est donnée en termes des fonctions de Green et Robin sur le domaine. On prouve que l'existence de solutions dépend des points critiques de la fonction susmentionnée augmentée d'une condition de non-dégénérescence. Enfin, on considère un problème non local dans le groupe de Heisenberg $H$. On s'intéresse à des propriétés de rigidité des solutions stables de $(-Delta_H)^s v = f(v)$ sur $H$, $s in (0,1)$. Une inégalité de type Poincaré connectée à un problème dégénéré dans $R^4_+$ est prouvée. Au travers d'une procédure d'extension, cette inégalité est utilisée pour donner un critère sous lequel les lignes de niveaux de la solution de l'EDP sont des surfaces minimales dans $H$
This work is devoted to nonlinear PDEs. The aim is to find regular solutions to some elliptic and hypo-elliptic PDEs and study their qualitative properties. The first part deals with the supercritical problem $$ -Delta u = lambda e^u,$$ $lambda > 0$, in an exterior domain under zero Dirichlet condition. A finite-dimensional reduction scheme provides the existence of infinitely many regular solutions whenever $lambda$ is sufficiently small.The second part is focused on the existence of bubbling solutions for the non-local equation $$ (-Delta)^s u =u^p, ,u>0,$$in a bounded, smooth domain under zero Dirichlet condition; where $0 0$ small). To this end, a finite-dimensional reduction scheme in suitable functional spaces is used, where the main part of the reduced function is given in terms of the Green's and Robin's functions of the domain. The existence of solutions depends on the existence of critical points of such a main term together with a non-degeneracy condition.In the third part, a non-local entire problem in the Heisenberg group $H$ is studied. The main interests are rigidity properties for stable solutions of $$(-Delta_H)^s v = f(v) in H,$$ $s in (0,1)$. A Poincaré-type inequality in connection with a degenerate elliptic equation in $R^4_+$ is provided. Through an extension (or ``lifting") procedure, this inequality will be then used to give a criterion under which the level sets of the above solutions are minimal surfaces in $H$, i.e. they have vanishing mean $H$-curvature
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Hofmann, B., and O. Scherzer. "Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800957.

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The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results.
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Ye, Jinglong. "Infinite semipositone systems." Diss., Mississippi State : Mississippi State University, 2009. http://library.msstate.edu/etd/show.asp?etd=etd-07072009-132254.

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Books on the topic "Operator equations, Nonlinear"

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Adomian, George. Nonlinear stochastic operator equations. Orlando: Academic Press, 1986.

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Adomian, G. Nonlinear stochastic operator equations. Orlando: Academic Press, 1986.

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A, Marchenko V. Nonlinear equations and operator algebras. Dordrecht: D. Reidel Pub. Co., 1988.

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Marchenko, Vladimir A. Nonlinear Equations and Operator Algebras. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2887-9.

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Krasnoselʹskiĭ, A. M. Asymptotics of nonlinearities and operator equations. Basel: Birkhäuser Verlag, 1995.

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Asimptotika nelineĭnosteĭ i operatornye uravnenii͡a︡. Moskva: "Nauka", 1992.

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Altman, Mieczyslaw. A unified theory of nonlinear operator and evolution equations with applications: A new approach to nonlinear partial differential equations. New York: M. Dekker, 1986.

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Krawcewicz, Wiesław. Contribution à la théorie des équations non linéaires dans les espaces de Banach. Warszawa: Państwowe Wydawn. Nauk., 1988.

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Rosen, I. Gary. Convergence of Galerkin approximations for operator Riccati equations--a nonlinear evolution equation approach. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1988.

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A unified theory of nonlinear operator and evolution equations with applications: A new approach to nonlinear partial differential equations. New York: M. Dekker, 1986.

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Book chapters on the topic "Operator equations, Nonlinear"

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Marchenko, Vladimir A. "Classes of Solutions to Nonlinear Equations." In Nonlinear Equations and Operator Algebras, 121–52. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2887-9_4.

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Marchenko, Vladimir A. "The General Scheme." In Nonlinear Equations and Operator Algebras, 1–21. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2887-9_1.

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Marchenko, Vladimir A. "Realization of General Scheme in Matrix Rings and N-Soliton Solutions." In Nonlinear Equations and Operator Algebras, 22–52. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2887-9_2.

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Marchenko, Vladimir A. "Realization of the General Scheme in Operator Algebras." In Nonlinear Equations and Operator Algebras, 53–120. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2887-9_3.

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O’Regan, Donal, and Maria Meehan. "Periodic Solutions for Operator Equations." In Existence Theory for Nonlinear Integral and Integrodifferential Equations, 204–15. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-4992-1_12.

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Tikhonov, A. N., A. S. Leonov, and A. G. Yagola. "Variational algorithms for solving nonlinear operator equations." In Nonlinear Ill-Posed Problems, 143–206. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-5167-4_3.

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Zgurovsky, M. Z., and V. S. Mel’nik. "Differential-Operator Equations and Inclusions." In Nonlinear Analysis and Control of Physical Processes and Fields, 97–147. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18770-4_4.

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Taylor, Michael E. "Function Space and Operator Theory for Nonlinear Analysis." In Partial Differential Equations I, 1–104. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7049-7_1.

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Taylor, Michael E. "Function Space and Operator Theory for Nonlinear Analysis." In Partial Differential Equations III, 1–88. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-4190-2_1.

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Sakhnovich, L. A. "Interpolation Problems, Inverse Spectral Problems and Nonlinear Equations." In Operator Theory and Complex Analysis, 292–304. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8606-2_15.

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Conference papers on the topic "Operator equations, Nonlinear"

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Bartsch, Thomas. "Critical equations for the polyharmonic operator." In Proceedings of the ICM 2002 Satellite Conference on Nonlinear Functional Analysis. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704283_0004.

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Nedzhibov, Gyurhan H., George Venkov, Ralitza Kovacheva, and Vesela Pasheva. "An approach to accelerate iterative methods for solving nonlinear operator equations." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '11): Proceedings of the 37th International Conference. AIP, 2011. http://dx.doi.org/10.1063/1.3664358.

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Precup, Radu, Alberto Cabada, Eduardo Liz, and Juan J. Nieto. "Componentwise compression-expansion conditions for systems of nonlinear operator equations and applications." In MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE: International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine. AIP, 2009. http://dx.doi.org/10.1063/1.3142943.

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Zhou, Yongquan, and Huajuan Huang. "Hybrid Artificial Fish School Algorithm Based on Mutation Operator for Solving Nonlinear Equations." In 2009 International Workshop on Intelligent Systems and Applications. IEEE, 2009. http://dx.doi.org/10.1109/iwisa.2009.5072896.

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5

Xu, Guang, Guocai Hu, and Junfeng Chen. "A New PSO Algorithm LM Operator Embedded in for Solving Systems of Nonlinear Equations." In 2014 6th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC). IEEE, 2014. http://dx.doi.org/10.1109/ihmsc.2014.137.

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ROGOSIN, S. V. "ON APPLICATION OF THE MONOTONE OPERATOR METHOD TO SOLVABILITY OF NONLINEAR SINGULAR INTEGRAL EQUATIONS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0119.

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Christiansen, Torben B., Harry B. Bingham, Allan P. Engsig-Karup, Guillaume Ducrozet, and Pierre Ferrant. "Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10861.

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A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichlet-to-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes.
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Kurdila, Andrew J., and Glenn Webb. "Identification of Thermal and Hysteretic Response of SMA Embedded Flexible Rods." 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/detc1995-0680.

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Abstract In this paper, the equations of motion governing the transient response of an elastomer rod with embedded shape memory alloy actuators are derived. The elastomeric flexural dynamics and elastomeric thermal dynamics are represented by a pair of parameter-dependent, coupled, partial differential equations. The response of the structural system exhibits strong hysteresis effects due to the nonlinear nature of the constitutive law of the SMA actuator. As opposed to previous work by the authors in which an explicit equation for the nonlinear constitutive law is utilized, the work herein utilizes an integral operator in a phenomenological representation of the hysteresis. Specifically, a static hysteresis operator is employed to represent the current-to-stress transformation in the SMA. The hysteresis operator consequently appears as a control influence operator in the system of governing partial differential equations. This paper presents a two-stage identification process to characterize the multivalued response associated with hysteresis. Preliminary experimental results validate the effectiveness of the method for the class of problems considered.
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Deshmukh, Venkatesh. "Stability Analysis and Computation of Solutions of Nonlinear Delay Differential Algebraic Equations With Time Periodic Coefficients." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35263.

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Stability theory of Nonlinear Delay Differential Algebraic Equations (DDAE) with periodic coefficients is proposed with a geometric interpretation of the evolution of the linearized system. First, a numerical algorithm based on direct integration by expansion in terms of Chebyshev polynomials is derived for linear analysis. The proposed algorithm is shown to have deeper connections with and computationally less cumbersome than the solution of the underlying semi-explicit system via a similarity transformation. The stability of time periodic DDAE systems is characterized by the spectral radius of a finite dimensional approximation or a “monodromy matrix” of a compact infinite dimensional operator. The monodromy operator is essentially a map of the Chebyshev coefficients of the state form the delay interval to the next adjacent interval of time. The monodromy matrix is obtained by a similarity transformation of the momodromy matrix of the associated semi-explicit system. The computations are entirely performed in the original system form to avoid cumbersome transformations associated with the semi-explicit system. Next, two computational algorithms are detailed for obtaining solutions of nonlinear DDAEs with periodic coefficients for consistent initial functions.
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Kurdila, A., and J. Li. "Relaxation Methods for Nonlinear Dynamics and Hysteresis Operators." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8062.

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Abstract Previous research has demonstrated that rigorous modeling and identification theory can be derived for structural dynamical models that incorporate control influence operators that are static Krasnoselskii-Pokrovskii integral hysteresis operators. Experimental evidence likewise has shown that some dynamic hysteresis models provide more accurate representations of a class of structural systems actuated by some active materials including shape memory alloys and piezoceramics. In this paper, we show that the representation of control influence operators via static hysteresis operators can be interpreted in terms of a homogeneous Young’s measure. Within this framework, we subsequently derive dynamic hysteresis operators represented in terms of Young’s measures that are parameterized in time. We show that the resulting integrodifferential equations are similar to the class of relaxed controls discussed by Warga [10], Garnkrelidze [24], and Roubicek [25]. The formulation presented here differs from that studied in [10], [24] and [25] in that the kernel of the hysteresis operator is a history dependent functional, as opposed to Caratheodory integral satisfying a growth condition. The theory presented provides representations of dynamic hysteresis operators that have provided good agreement with experimental behavior in some active materials.
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Reports on the topic "Operator equations, Nonlinear"

1

Carasso, Alfred S. Compensating Operators and Stable Backward in Time Marching in Nonlinear Parabolic Equations. National Institute of Standards and Technology, November 2013. http://dx.doi.org/10.6028/nist.ir.7967.

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