Overview
- Examines the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems
- Self-contained and up-to-date, taking special care on the didactical preparation of the material
- Devoted to problems that are intensively studied but have not been treated in depth in the book literature so far
Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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About this book
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.
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Keywords
Table of contents (5 chapters)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Superlinear Parabolic Problems
Book Subtitle: Blow-up, Global Existence and Steady States
Authors: Prof. Dr. Pavol Quittner, Prof. Dr. Philippe Souplet
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-3-030-18222-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-18220-5Published: 26 June 2019
eBook ISBN: 978-3-030-18222-9Published: 13 June 2019
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 2
Number of Pages: XXII, 719
Number of Illustrations: 15 b/w illustrations
Topics: Partial Differential Equations, Potential Theory, Functional Analysis