
Strongly Coupled Parabolic and Elliptic Systems
Existence and Regularity of Strong and Weak Solutions
- 195 pages
- English
- PDF
- Available on iOS & Android
Strongly Coupled Parabolic and Elliptic Systems
Existence and Regularity of Strong and Weak Solutions
About this book
Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included.
Contents
Interpolation GagliardoāNirenberg inequalities
The parabolic systems
The elliptic systems
Cross-diffusion systems of porous media type
Nontrivial steady-state solutions
The duality RBMO( ? )ā H 1( ? )|
Some algebraic inequalities
Partial regularity
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Information
Table of contents
- Preface
- Contents
- 1. Introduction
- 2. Interpolation GagliardoāNirenberg inequalities
- 3. The parabolic systems
- 4. The elliptic systems
- 5. Cross-diffusion systems of porous media type
- 6. Nontrivial steady-state solutions
- A The duality RBMO(μ)āH1(μ)
- B Some algebraic inequalities
- C Partial regularity
- Bibliography
- Index