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 85
... respect to L ) if every solution u of class C of Lu = 0 in R vanishes if its Cauchy data on Z vanish . ‡ The uniqueness theorem just proved permits to construct domains of determinacy with the help of suitable non - characteristic ...
... respect to L ) if every solution u of class C of Lu = 0 in R vanishes if its Cauchy data on Z vanish . ‡ The uniqueness theorem just proved permits to construct domains of determinacy with the help of suitable non - characteristic ...
Página 167
... respect to the norm |||||| also are Cauchy sequences with respect to the norm || v || , it follows that ( A ̄1v , w ) defines a bounded linear functional on H. By the representation theorem ( p . 118 ) we can then find an element U in H ...
... respect to the norm |||||| also are Cauchy sequences with respect to the norm || v || , it follows that ( A ̄1v , w ) defines a bounded linear functional on H. By the representation theorem ( p . 118 ) we can then find an element U in H ...
Página 225
... respect to t it follows for any & > 0 that dнW ( x , t ) – dĥW ( x , t ) = dμW ( x , ε ) − dĥW ( x , ɛ ) - + Sz dz ... respect to H , and hence also with respect to x , and that Wxx ( x + H , t ) = WHH = [ ' ( 2zw ( x + zH , t ) + Hz2w ...
... respect to t it follows for any & > 0 that dнW ( x , t ) – dĥW ( x , t ) = dμW ( x , ε ) − dĥW ( x , ɛ ) - + Sz dz ... respect to H , and hence also with respect to x , and that Wxx ( x + H , t ) = WHH = [ ' ( 2zw ( x + zH , t ) + Hz2w ...
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