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 9
... characteristic direction , matters for the P.D.E. ( 4.2 ) . Since ( u ,,,, -1 ) constitute direction numbers of the ... curves which at each point are tangent to that direction field . Along a characteristic curve the relation dx dy ...
... characteristic direction , matters for the P.D.E. ( 4.2 ) . Since ( u ,,,, -1 ) constitute direction numbers of the ... curves which at each point are tangent to that direction field . Along a characteristic curve the relation dx dy ...
Página 10
... characteristic curve , which is its range ) . If a surface S : z = u ( x , y ) is a union of characteristic curves , then S is an integral surface . For then through any point P of S there passes a characteristic curve y contained in S ...
... characteristic curve , which is its range ) . If a surface S : z = u ( x , y ) is a union of characteristic curves , then S is an integral surface . For then through any point P of S there passes a characteristic curve y contained in S ...
Página 35
... characteristic curve y is given implicitly by an equation ( x , y ) = const ... curves in the hyperbolic case , one in the parabolic case , and none in the ... characteristic curves are closely associated with the propagation of certain ...
... characteristic curve y is given implicitly by an equation ( x , y ) = const ... curves in the hyperbolic case , one in the parabolic case , and none in the ... characteristic curves are closely associated with the propagation of certain ...
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