Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States / Edition 2

by Prof. Dr. Pavol Quittner, Prof. Dr. Philippe Souplet

Overview

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology.

The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whosestudy requires new ideas. Many open problems are mentioned and commented.

The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics.

The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.

Product Details

ISBN-13:	9783030182205
Publisher:	Springer International Publishing
Publication date:	06/13/2019
Series:	Birkh�user Advanced Texts Basler Lehrb�cher
Edition description:	Second Edition 2019
Pages:	719
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Pavol Quittner is Full Professor of Mathematics at the Comenius University in Bratislava. He received his PhD in Mathematics from the Charles University in Prague in 1987. His research interests focus on nonlinear partial differential equations.

Philippe Souplet is Full Professor of Mathematics and Head of the Mathematics Research Department (LAGA, CNRS UMR 7539) at Université Paris 13. He received his PhD in Mathematics from Université Paris 6. His research interests focus on nonlinear partial differential equations.

Table of Contents

Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.

Editorial Reviews

From the reviews:

“This book was written by two authors who in the past have made numerous substantial contributions to this field … . A list of applicable tricks, tools and techniques proves very helpful. Quittner and Souplet have opened their fat bag and let the reader profit from their large collection of methods described in this appendix. …The authors have put a lot of hard work into this book, and their efforts have certainly paid off. … recommended to anyone interested in this important and extensive field.” (R. Sperb, Zeitschrift für angewandte Mathematik und Physik, Vol. 60, 2009)

From the Publisher