Partial Differential EquationsSpringer, 1982 - 249 páginas This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy 's example of a linear equation without solutions. |
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Página 65
... uniquely in N if we know the Daf ( z ) for all a Є Z " . In particular f is determined uniquely in N by its values in any non - empty open subset of S. PROOF . Let g , hЄ C ° ( N ) and let Dag ( z ) = Dah ( z ) for all a € Z " . Writef ...
... uniquely in N if we know the Daf ( z ) for all a Є Z " . In particular f is determined uniquely in N by its values in any non - empty open subset of S. PROOF . Let g , hЄ C ° ( N ) and let Dag ( z ) = Dah ( z ) for all a € Z " . Writef ...
Página 88
... uniquely by its Cauchy data on xn = = 0 . = = 2. Let Lu O be a linear system with constant coefficients for functions u = u ( x1 , ... , x ) . Let Z be a solid ellipsoid in the plane x , 0. Let y be a point of R " with yn > 0 , and let ...
... uniquely by its Cauchy data on xn = = 0 . = = 2. Let Lu O be a linear system with constant coefficients for functions u = u ( x1 , ... , x ) . Let Z be a solid ellipsoid in the plane x , 0. Let y be a point of R " with yn > 0 , and let ...
Página 95
... uniquely . A solution uЄC2 ( ) of the Neumann problem is determined uniquely within an additive constant . ( Notice also that since an the solution of the Neumann problem can only exist if the data satisfy termined condition ( 1.3 ) ...
... uniquely . A solution uЄC2 ( ) of the Neumann problem is determined uniquely within an additive constant . ( Notice also that since an the solution of the Neumann problem can only exist if the data satisfy termined condition ( 1.3 ) ...
Contenido
Chapter | 1 |
Examples | 2 |
Analytic Solution and Approximation Methods in a Simple Example Problems 4 Quasilinear Equations | 4 |
Derechos de autor | |
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analytic functions assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f fundamental solution Gårding Gårding's inequality given harmonic function heat equation hence Hint Ho(N holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix maximum principle neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof real analytic real numbers satisfies scalar Show solution u(x,t solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ