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Birkhäuser

Linear and Quasilinear Parabolic Problems

Volume I: Abstract Linear Theory

  • Book
  • © 1995

Overview

Authors:
  1. Herbert Amann

    1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland

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Part of the book series: Monographs in Mathematics (MMA, volume 89)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxxv
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  2. Notation and Conventions

    • Herbert Amann
    Pages 1-7

  3. Generators and Interpolation

    • Herbert Amann
    Pages 9-37

  4. Cauchy Problems and Evolution Operators

    • Herbert Amann
    Pages 39-85

  5. Maximal Regularity

    • Herbert Amann
    Pages 87-191

  6. Variable Domains

    • Herbert Amann
    Pages 193-247

  7. Scales of Banach Spaces

    • Herbert Amann
    Pages 249-319

  8. Back Matter

    Pages 321-338
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Keywords

About this book

In this treatise we present the semigroup approach to quasilinear evolution equa­ of parabolic type that has been developed over the last ten years, approxi­ tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic­ ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille­ Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

Authors and Affiliations

  • Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Herbert Amann

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