Hyperbolic Partial Differential Equations

Serge Alinhac

ISBN 10: 038787822X / ISBN 13: 9780387878225

Published by Springer New York Jun 2009, 2009

About this Item

Neuware - The aim of this book is to present hyperbolic partial di erential equations at an elementary level. In fact, the required mathematical background is only a third year university course on di erential calculus for functions of several variables. No functional analysis knowledge is needed, nor any distribution theory (with the exception of shock waves mentioned below). k All solutions appearing in the text are piecewise classical C solutions. Beyond the simpli cations it allows, there are several reasons for this choice: First, we believe that all main features of hyperbolic partial d- ferential equations (PDE) (well-posedness of the Cauchy problem, nite speed of propagation, domains of determination, energy inequalities, etc. ) canbedisplayedinthiscontext. Wehopethatthisbookitselfwillproveour belief. Second,allproperties,solutionformulas,andinequalitiesestablished here in the context of smooth functions can be readily extended to more general situations (solutions in Sobolev spaces or temperate distributions, etc. ) by simple standard procedures of functional analysis or distribution theory, which are 'external' to the theory of hyperbolic equations: The deep mathematical content of the theorems is already to be found in the statements and proofs of this book. The last reason is this: We do hope that many readers of this book will eventually do research in the eld that seems to us the natural continuation of the subject: nonlinear hyp- bolic systems (compressible uids, general relativity theory, etc. ). Seller Inventory # 9780387878225

Bibliographic Details

Title: Hyperbolic Partial Differential Equations

Publisher: Springer New York Jun 2009

Publication Date: 2009

Binding: Taschenbuch

Condition: Neu

About this title

Synopsis:

This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. It includes more than 100 exercises, along with "do-it-yourself" instructions for the proofs of many theorems.

From the Back Cover:

Serge Alinhac (1948–) received his PhD from l'Université Paris-Sud XI (Orsay). After teaching at l'Université Paris Diderot VII and Purdue University, he has been a professor of mathematics at l'Université Paris-Sud XI (Orsay) since 1978. He is the author of Blowup for Nonlinear Hyperbolic Equations (Birkhäuser, 1995) and Pseudo-differential Operators and the Nash–Moser Theorem (with P. Gérard, American Mathematical Society, 2007). His primary areas of research are linear and nonlinear partial differential equations.

 

This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions.

Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.