Linear and quasi-linear evolution equations in Hilbert spaces / Pascal Cherrier, Albert Milani.

Format:

Book

Author/Creator:

Cherrier, Pascal, 1950- author.

Milani, A. (Albert), author.

Series:

Graduate studies in mathematics ; Volume 135.

Graduate Studies in Mathematics ; Volume 135

Language:

English

Subjects (All):

Initial value problems.

Differential equations, Hyperbolic.

Evolution equations.

Hilbert space.

Physical Description:

1 online resource (378 p.)

Edition:

1st ed.

Other Title:

Linear and quasilinear evolution equations in Hilbert spaces

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

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 well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point 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 quasi-linear 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 self-contained. 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.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Functional framework""; ""Linear equations""; ""Quasi-linear equations""; ""Global existence""; ""Asymptotic behavior""; ""Singular convergence""; ""Maxwell�s and von Karman�s equations""; ""List of function spaces""; ""Bibliography""; ""Index""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-8218-8784-X

OCLC:

922981884