
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Graduate Studies in Mathematics 2012; 377 pp; hardcover Volume: 135 ISBN10: 0821875760 ISBN13: 9780821875766 List Price: US$75 Member Price: US$60 Order Code: GSM/135 See also: Lectures on Elliptic and Parabolic Equations in Hölder Spaces  N V Krylov Lectures on Elliptic and Parabolic Equations in Sobolev Spaces  N V Krylov  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. Readership Graduate students and research mathematicians interested in partial differential equations. 


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