Hyperbolic Partial Differential Equations

Serge Alinhac

2009年6月 · Springer Science & Business Media

電子書

150

頁數

評分和評論未經驗證瞭解詳情

關於這本電子書

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. ).

關於作者

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.