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Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States
Buch | Hardcover
XII, 584 Seiten
2007 | 2007
Springer Basel (Verlag)
978-3-7643-8441-8 (ISBN)

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Superlinear Parabolic Problems - Pavol Quittner, Philippe Souplet
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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.

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

Erscheint lt. Verlag 16.8.2007
Reihe/Serie Birkhäuser Advanced Texts /Basler Lehrbücher
Zusatzinfo XII, 584 p.
Verlagsort Basel
Sprache englisch
Maße 170 x 250 mm
Gewicht 1096 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte A-priori bounds • blow-up • Cauchy problem • Dirichlet problem • parabolic problem • Parabolische Differentialgleichungen • partial differential equation
ISBN-10 3-7643-8441-7 / 3764384417
ISBN-13 978-3-7643-8441-8 / 9783764384418
Zustand Neuware
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