ENGLISH

Strongly Coupled Parabolic and Elliptic Systems: Existence and Regularity of Strong and Weak Solutions

By Dung Le

Book information

Publisher
de Gruyter
Year
2018
ISBN
3110607158, 9783110607154
Language
english
Format
PDF
Filesize
1 MB (1445739 bytes)
Series
De Gruyter Series in Nonlinear Analysis & Applications, 28
Edition
1
Pages
185\199
Time added
2021-08-29 03:28:00

Description

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 GagliardoNirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO()H1()| Some algebraic inequalities Partial regularity 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(μ)–H1(μ) B Some algebraic inequalities C Partial regularity Bibliography Index

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