Notices of the American Mathematical Society

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. August 2012-front cover MacKichan Software Math In Moscow Scholarship Program WebAssign August 2012 Table of Contents Opinion--What's a Math Educator to Do?, Solomon Garfunkel Letters to the Editor AMS Headlines and Deadlines for Students Galois for 21st-Century Readers, Harold M. Edwards Right or Wrong? That Is the Question, M. Dedo and L. Sferch Drowning in the Data Deluge, George E. Andrews A Tribute to Nigel J. Kalton (1946-2010), Peter G. Casazza, Coordinating Editor WHAT IS...an Octopus Decomposition? MAA Electronic Bookstore Math Girls--A Book Review, reviewed by Mari Abe and Mei Kobayashi Magical Mathematics--A Book Review, reviewed by Donovan H. Van Osdol Daubechies Awarded Nemmers Prize Doceamus: Solutions in Search of Problems, Jeremy F. Alm and David A. Andrews Scripta Manent: Copyright in Academic Writings: Yours to Have and to Hold (and From Which a Publishing Contract Need Not Make You Part), Jane Ginsburg Mathematics People Mathematics Opportunities Inside the AMS Reference and Booklist Doctoral Degrees Conferred 2010-2011 Voting Information for 2012 AMS Election Report of the Executive Director, State of the AMS, 2012 Mathematics Calendar New Publications Offered by the AMS Classified Advertisements Meetings and Conferences of the AMS Meetings and Conferences Table of Contents Summer Reads from Cambridge University Press AMS Grad Student Travel Grants New Releases from the AMS