Progress in nonlinear differential equations and their applications - 9781461273967 - a stability technique for evolution partial differential equations: a dynamical systems approach: 56 di galaktionov, victor a.; vázquez, juan luis (13 risultati)

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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -\* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations.\* Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs.\* Well-organized text with detailed index and bibliography, suitable as a course text or reference volume. 400 pp. Englisch.…

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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equationsWritten by established mathematicians at the forefront of their field, this blend of delicate analysis and broad .…

Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book introduces a new, state-of-the-art method for the study of asymptotic behavior of solutions for evolution equations. The underlying theory hinges on a new stability result, which is presented in detail; also included is a review of basic techniques---many original to the authors---for the solution of nonlinear diffusion equations. Subsequent chapters feature a self-contained analysis of specific equations whose solutions depend on the stability theorem; a variety of estimation techniques for solutions of semi- and quasilinear parabolic equations are provided as well.With its carefully-constructed theorems, proofs, and references, the text is appropriate for students and researchers in physics and mathematics who have basic knowledge of PDEs and some prior acquaintance with evolution equations. Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear partial differential equations.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 400 pp. Englisch.…