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Birkhäuser Advanced Texts Basler Lehrbücher

Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States

Authors: Quittner, Pavol, Souplet, Philippe

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  • 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
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About this Textbook

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, whose study 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.

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.




Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $69.99
price for USA in USD
  • ISBN 978-3-030-18222-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-3-030-18220-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Superlinear Parabolic Problems
Book Subtitle
Blow-up, Global Existence and Steady States
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-18222-9
DOI
10.1007/978-3-030-18222-9
Hardcover ISBN
978-3-030-18220-5
Series ISSN
1019-6242
Edition Number
2
Number of Pages
XXII, 719
Number of Illustrations
15 b/w illustrations
Topics

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