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Strongly Coupled Parabolic and Elliptic Systems

Existence and Regularity of Strong and Weak Solutions

Dung Le

PDF
ca. 139,95 €
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De Gruyter img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Analysis

Beschreibung

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(μ)–H1(μ)|
Some algebraic inequalities
Partial regularity

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Schlagwörter

Gekoppeltes System, Diffusion, System von partiellen Differentialgleichungen, Nichtlineare elliptische Differentialgleichung, Nichtlineare parabolische Differentialgleichung