Hyperbolic partial differential equations / Serge Alinhac.
"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 a...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Dordrecht ; New York :
Springer-Verlag,
[2009]
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| Series: | Universitext.
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| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | "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. )."--Publisher's website. |
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| Physical Description: | 1 online resource. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 038787822X 9780387878225 038787951X 9780387879512 0387878238 9780387878232 1282292633 9781282292635 |