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. |
Dentro del libro
Resultados 1-3 de 61
Página 49
... bounded vectors v ( x , t ) with domain in the strip 0 < t < 7 , using in C the " maximum norm " : || v || = sup | vx ( x , t ) | . k = 1 , ... , N x ; 0 < t < T ( 5.25 ) The norm || S || of the operator S ( the supremum of || Sv || for ...
... bounded vectors v ( x , t ) with domain in the strip 0 < t < 7 , using in C the " maximum norm " : || v || = sup | vx ( x , t ) | . k = 1 , ... , N x ; 0 < t < T ( 5.25 ) The norm || S || of the operator S ( the supremum of || Sv || for ...
Página 152
... bounded . Using the fact that the roots of a polynomial with highest coefficient 1 depend continu- ously on the ... bounded uniformly for all sufficiently large p = | $ | . By ( 2.34 ) λ and Imλ also are bounded for bounded | ] . Thus ...
... bounded . Using the fact that the roots of a polynomial with highest coefficient 1 depend continu- ously on the ... bounded uniformly for all sufficiently large p = | $ | . By ( 2.34 ) λ and Imλ also are bounded for bounded | ] . Thus ...
Página 230
... bounded h / k would correspond to a uniformly bounded domain of dependence for v ' ( x , t ) on f , and hence also for u ( x , t ) , whereas the example of the heat equation shows that the domain of dependence of u ( x , t ) on the ...
... bounded h / k would correspond to a uniformly bounded domain of dependence for v ' ( x , t ) on f , and hence also for u ( x , t ) , whereas the example of the heat equation shows that the domain of dependence of u ( x , t ) on the ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
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Términos y frases comunes
assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Cauchy-Kowalevski Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders determined uniquely difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f(x fundamental solution Gårding given Green's identity heat equation hence Hint holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof quasi-linear real numbers satisfies scalar second derivatives Show solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ