Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations

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Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations

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Author : Messoud Efendiev
language : en
Publisher: Springer
Release Date : 2018-10-17

Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations written by Messoud Efendiev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-17 with Mathematics categories.

This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.

Linear And Nonlinear Non Fredholm Operators

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Author : Messoud Efendiev
language : en
Publisher: Springer Nature
Release Date : 2023-02-04

Linear And Nonlinear Non Fredholm Operators written by Messoud Efendiev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-04 with Mathematics categories.

This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics. First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear – nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of “stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood. Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local – nonlocal diffusion as well as terms for transport and nonlinear interactions.

A Stability Technique For Evolution Partial Differential Equations

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Author : Victor A. Galaktionov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A Stability Technique For Evolution Partial Differential Equations written by Victor A. Galaktionov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

common feature is that these evolution problems can be formulated as asymptoti cally small perturbations of certain dynamical systems with better-known behaviour. Now, it usually happens that the perturbation is small in a very weak sense, hence the difficulty (or impossibility) of applying more classical techniques. Though the method originated with the analysis of critical behaviour for evolu tion PDEs, in its abstract formulation it deals with a nonautonomous abstract differ ential equation (NDE) (1) Ut = A(u) + C(u, t), t > 0, where u has values in a Banach space, like an LP space, A is an autonomous (time-independent) operator and C is an asymptotically small perturbation, so that C(u(t), t) ~ ° as t ~ 00 along orbits {u(t)} of the evolution in a sense to be made precise, which in practice can be quite weak. We work in a situation in which the autonomous (limit) differential equation (ADE) Ut = A(u) (2) has a well-known asymptotic behaviour, and we want to prove that for large times the orbits of the original evolution problem converge to a certain class of limits of the autonomous equation. More precisely, we want to prove that the orbits of (NDE) are attracted by a certain limit set [2* of (ADE), which may consist of equilibria of the autonomous equation, or it can be a more complicated object.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Partial Differential Equations

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Author : Bogdan Bojarski
language : en
Publisher:
Release Date : 1992

Partial Differential Equations written by Bogdan Bojarski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Differential equations, Partial categories.

Differential And Integral Equations

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Author :
language : en
Publisher:
Release Date : 2001

Differential And Integral Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Differential equations categories.

Nonlocal And Nonlinear Diffusions And Interactions New Methods And Directions

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Author : José Antonio Carrillo
language : en
Publisher: Springer
Release Date : 2017-10-03

Nonlocal And Nonlinear Diffusions And Interactions New Methods And Directions written by José Antonio Carrillo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-03 with Mathematics categories.

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.

Handbook Of Numerical Analysis

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Author : Philippe G. Ciarlet
language : en
Publisher: Gulf Professional Publishing
Release Date : 1990

Handbook Of Numerical Analysis written by Philippe G. Ciarlet and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Numerical analysis categories.

Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications

Reviews In Partial Differential Equations 1980 86 As Printed In Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 1988

Reviews In Partial Differential Equations 1980 86 As Printed In Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Differential equations, Partial categories.

Physics Briefs

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Author :
language : en
Publisher:
Release Date : 1993

Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Physics categories.