Linear and quasilinear parabolic systems : Sobolev space theory
著者
書誌事項
Linear and quasilinear parabolic systems : Sobolev space theory
（Mathematical surveys and monographs, v. 251）
American Mathematical Society, c2020
- : pbk
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注記
Includes bibliographical references (p. 221-223) and indexes
内容説明・目次
内容説明
This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
目次
Introduction
Differential equations in Hilbert space
Linear parabolic systems: Basic theory
Elliptic systems: Higher order regularity
Parabolic systems: Higher order regularity
Applications to quasilinear systems
Selected topics in analysis
Bibliography
Index
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