Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States

  • Pavol Quittner
  • Philippe Souplet

Part of the Birkhäuser Advanced Texts / Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-5
  3. Pages 251-312
  4. Pages 377-427
  5. Back Matter
    Pages 429-584

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, 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.


A-priori bounds Cauchy problem Dirichlet problem blow-up parabolic problem partial differential equation

Authors and affiliations

  • Pavol Quittner
    • 1
  • Philippe Souplet
    • 2
  1. 1.Department of Applied Mathematics and StatisticsComenius UniversityBratislavaSlovakia
  2. 2.Laboratoire Analyse Géométrie et Applications UMR CNRS 7539 -Institut GaliléeUniversité Paris-NordVilletaneuseFrance

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