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 viii
... Method " ) 111 116 5. Solution of the Dirichlet Problem by Hilbert - Space Methods 117 125 Problems Problems Chapter 5 Hyperbolic Equations in Higher Dimensions 1. The Wave Equation in n - Dimensional Space ( a ) The method of spherical ...
... Method " ) 111 116 5. Solution of the Dirichlet Problem by Hilbert - Space Methods 117 125 Problems Problems Chapter 5 Hyperbolic Equations in Higher Dimensions 1. The Wave Equation in n - Dimensional Space ( a ) The method of spherical ...
Página ix
... method of plane waves Problems 3. Symmetric Hyperbolic Systems ( a ) The basic energy inequality Problems ( b ) Existence of solutions by the method of finite differences 139 142 143 143 145 145 156 157 158 161 163 163 169 172 Problems ...
... method of plane waves Problems 3. Symmetric Hyperbolic Systems ( a ) The basic energy inequality Problems ( b ) Existence of solutions by the method of finite differences 139 142 143 143 145 145 156 157 158 161 163 163 169 172 Problems ...
Página 133
... method of descent In this method solutions of a partial differential equation are obtained by considering them as special solutions of another equation which involves more independent variables , and can be solved . For example a ...
... method of descent In this method solutions of a partial differential equation are obtained by considering them as special solutions of another equation which involves more independent variables , and can be solved . For example a ...
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