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 20
... ( Figure 1.3 ) . Each possible tangent plane touches the Monge cone along a certain generator . In this way the partial differential equation ( 7.1 ) defines a field of cones . A surface z = u ( x , y ) is an integral surface if at each ...
... ( Figure 1.3 ) . Each possible tangent plane touches the Monge cone along a certain generator . In this way the partial differential equation ( 7.1 ) defines a field of cones . A surface z = u ( x , y ) is an integral surface if at each ...
Página 42
... Figure 2.2 Geometrically , for any parallelogram ABCD in the xt - plane bounded by four characteristic lines , ( see Figure 2.4 ) , the sums of the values of u in opposite vertices are equal , that is , u ( A ) + u ( C ) = u ( B ) + u ...
... Figure 2.2 Geometrically , for any parallelogram ABCD in the xt - plane bounded by four characteristic lines , ( see Figure 2.4 ) , the sums of the values of u in opposite vertices are equal , that is , u ( A ) + u ( C ) = u ( B ) + u ...
Página 131
Fritz John. ( v , t ) y ct t = 0 Figure 5.2 thickness 2p expanding with velocity c . ( See Figure 5.3 . ) This accounts for the possibility of " sharp " signals being transmitted in accordance with equation ( 1.1 ) in three dimensions ...
Fritz John. ( v , t ) y ct t = 0 Figure 5.2 thickness 2p expanding with velocity c . ( See Figure 5.3 . ) This accounts for the possibility of " sharp " signals being transmitted in accordance with equation ( 1.1 ) in three dimensions ...
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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Términos y frases comunes
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