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 65
... theorem : Theorem . Let f = C ( N ) where N is a connected open set * in R " . Let z € N. Then f is determined uniquely in N if we know the Daf ( z ) for all a Є Z " . In particular f is determined uniquely in N by its values in any non ...
... theorem : Theorem . Let f = C ( N ) where N is a connected open set * in R " . Let z € N. Then f is determined uniquely in N if we know the Daf ( z ) for all a Є Z " . In particular f is determined uniquely in N by its values in any non ...
Página 67
... theorem works with the method of majorants , in which problems are compared with others that in some ways behave worse but can be solved explicitly . In this way complicated estimates are replaced by simple explicit manipulations ...
... theorem works with the method of majorants , in which problems are compared with others that in some ways behave worse but can be solved explicitly . In this way complicated estimates are replaced by simple explicit manipulations ...
Página 247
... theorem Hodograph method 40 118 , 125 Holmgren's uniqueness theorem 80-87 , 144 Homogeneous function , Euler equation 15 , 16 Huygens ' principle 131 , 134 wave front generation 31 , 130 Hyperbolic 145 , 155 constant coefficients first ...
... theorem Hodograph method 40 118 , 125 Holmgren's uniqueness theorem 80-87 , 144 Homogeneous function , Euler equation 15 , 16 Huygens ' principle 131 , 134 wave front generation 31 , 130 Hyperbolic 145 , 155 constant coefficients first ...
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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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