A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach: 56 (Progress in Nonlinear Differential Equations and Their Applications, 56) - Hardcover

Galaktionov, Victor A.; Vázquez, Juan Luis

Hardcover

ISBN 10: 0817641467 ISBN 13: 9780817641467

Publisher: Birkhäuser, 2003

Synopsis

* 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.

About this title

Review

"The authors are famous experts in the field of PDEs and blow-up techniques. In this book they present a stability theorem, the so-called S-theorem, and show, with several examples, how it may be applied to a wide range of stability problems for evolution equations. The book [is] aimed primarily aimed at advanced graduate students."

―Mathematical Reviews

"The book is very interesting and useful for researchers and students in mathematical physics...with basic knowledge in partial differential equations and functional analysis. A comprehensive index and bibliography are given" ---Revue Roumaine de Mathématiques Pures et Appliquées

Synopsis

This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of nonlinear diffusion equations. The underlying theory hinges on a new stability result, formulated in the abstract setting of infinite-dimensional dynamical systems, which states that under certain hypotheses, the omega-limit set of a perturbed dynamical system is stable under arbitrary asymptotically small perturbations.The Stability Theorem is examined in detail in the first chapter, followed by a review of basic results and methods---many original to the authors---for the solution of nonlinear diffusion equations. Further chapters provide a self-contained analysis of specific equations, with carefully-constructed theorems, proofs, and references. In addition to the derivation of interesting limiting behaviors, the book features a variety of estimation techniques for solutions of semi- and quasilinear parabolic equations.Written by established mathematicians at the forefront of the field, this work is a blend of delicate analysis and broad application, appropriate for graduate students and researchers in physics and mathematics who have basic knowledge of PDEs, ordinary differential equations, functional analysis, and some prior acquaintance with evolution equations.

It is ideal for a course or seminar in evolution equations and asymptotics, and the book's comprehensive index and bibliography will make it useful as a reference volume as well.

Edition details

• Publisher: Birkhäuser
• Publication date: 2003
• Language: English
• ISBN 10: 0817641467
• ISBN 13: 9780817641467
• Binding: Hardcover
• Number of pages: 377