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 45
... solution u ( x , t ) of ( 4.1 ) , ( 4.8 ) has compact support in x for each fixed t . Show that the functions F , G in the decomposition ( 4.5 ) for u can be of compact support only when f∞∞ 8 ( § ) d = 0 . 2. Let a be a constant · c ...
... solution u ( x , t ) of ( 4.1 ) , ( 4.8 ) has compact support in x for each fixed t . Show that the functions F , G in the decomposition ( 4.5 ) for u can be of compact support only when f∞∞ 8 ( § ) d = 0 . 2. Let a be a constant · c ...
Página 77
... solutions is unrealistic . It implies that the solution is determined globally by local conditions near one point , and makes it impossible to describe phenomena that do not interact instantaneously with the whole universe ( hence it ...
... solutions is unrealistic . It implies that the solution is determined globally by local conditions near one point , and makes it impossible to describe phenomena that do not interact instantaneously with the whole universe ( hence it ...
Página 145
... solution ug of a standard problem corresponds to the data ( 2.5 ) . For a nonchar- acteristic initial plane t = 0 the matrix P ( 0 , 1 ) is nondegenerate , and we can assume that P ( 0,1 ) = I ( 2.12 ) is the unit matrix . The solution ...
... solution ug of a standard problem corresponds to the data ( 2.5 ) . For a nonchar- acteristic initial plane t = 0 the matrix P ( 0 , 1 ) is nondegenerate , and we can assume that P ( 0,1 ) = I ( 2.12 ) is the unit matrix . The solution ...
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