Strongly coupled parabolic and elliptic systems : existence and regularity of strong and weak solutions
Control theory Coupled mode theory Differential equations, Elliptic Differential equations, Parabolic Differential equations, Partial e-böcker
Walter de Gruyter GmbH
2019
EISBN 9783110607178
Frontmatter.
Preface.
Contents.
1. Introduction.
2. Interpolation Gagliardo-Nirenberg 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(o)-H1(o).
B Some algebraic inequalities.
C Partial regularity.
Bibliography.
Index
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 Gagliardo-Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(o)-H1(o).
Preface.
Contents.
1. Introduction.
2. Interpolation Gagliardo-Nirenberg 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(o)-H1(o).
B Some algebraic inequalities.
C Partial regularity.
Bibliography.
Index
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 Gagliardo-Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(o)-H1(o).
