Alinhac Hyperbolic Partial Differential Equations

1. Auflage 2009
ISBN: 978-0-387-87823-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 150 Seiten, eBook

Reihe: Universitext

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. ).

Zielgruppe

Graduate

Autoren/Hrsg.

Alinhac, Serge

Inhaltsverzeichnis

Vector Fields and Integral Curves.- Operators and Systems in the Plane.- Nonlinear First Order Equations.- Conservation Laws in One-Space Dimension.- The Wave Equation.- Energy Inequalities for the Wave Equation.- Variable Coefficient Wave Equations and Systems.

Über Autor(innen)

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.