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Linear and quasilinear parabolic systems : Sobolev space theory /

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 quasilinea...

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Bibliographic Details
Main Authors: Hoff, David Charles, 1948- (Author)
Published: American Mathematical Society,
Publisher Address: Providence, Rhode Island :
Publication Dates: [2020]
Literature type: Book
Language: English
Series: Mathematical surveys and monographs, volume 251
Subjects:
Differential equations, Partial.
Differential equations, Parabolic.
Summary: 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.--Publisher's information.
Carrier Form: xi, 226 pages ; 26 cm.
Bibliography: Includes bibliographical references (pages 221-223) and index.
ISBN: 9781470461614 (paperback) :
1470461617 (paperback)
9781470463205 (electronic book)
1470463202 (electronic book)
Index Number: QA377
CLC: O175.26
Call Number: O175.26/H698
Contents: 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 -- Appendix: Selected Topics in Analysis.

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