Linear and quasilinear evolution equations in Hilbert spaces
 Author/Creator
 Cherrier, Pascal, 1950
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xviii, 377 p. ; 25 cm.
 Series
 Graduate studies in mathematics ; v. 135.
Access
Available online

Stacks

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QA378 .C44 2012

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QA378 .C44 2012
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Contributors
 Contributor
 Milani, A. (Albert)
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong wellposedness and asymptotic behavior results for the Cauchy problem for quasilinear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasilinear equations, by means of a linearization and fixedpoint technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasilinear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely selfcontained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Pascal Cherrier, Albert Milani.
 Title Variation
 Linear and quasilinear evolution equations in Hilbert spaces
 Series
 Graduate studies in mathematics ; v. 135
 ISBN
 0821875760
 9780821875766