Hyperbolic Partial Differential Equations(1st Edition)
Authors:
Serge Alinhac
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Solution Manual Includes
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ISBN: 038787822X, 978-0387878225
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Book Price $0 : 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 â??externalâ? 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. ).
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