Description

Book Synopsis

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

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

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    A Hardback by Dung Le

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      View other formats and editions of Strongly Coupled Parabolic and Elliptic Systems: Existence and Regularity of Strong and Weak Solutions by Dung Le

      Publisher: De Gruyter
      Publication Date: 05/11/2018
      ISBN13: 9783110607154, 978-3110607154
      ISBN10:

      Description

      Book Synopsis

      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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