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 61
... Analytic Functions and the Cauchy - Kowalevski Theorem * ( 2.32 ) This theorem quite generally asserts the local existence of solutions of the non - characteristic Cauchy problem , provided the equation and data are analytic . Hence we ...
... Analytic Functions and the Cauchy - Kowalevski Theorem * ( 2.32 ) This theorem quite generally asserts the local existence of solutions of the non - characteristic Cauchy problem , provided the equation and data are analytic . Hence we ...
Página 69
... function y = h ( x ) analytic at 0 to satisfy y = g ( x , y ) are a set of recursion relations Ca = P ( D38g ( 0,0 ) , c ) ; Co = 0 ( 3.20 ) = where c1 = Dh ( O ) , | 3 Real Analytic Functions and the Cauchy - Kowalevski Theorem 69.
... function y = h ( x ) analytic at 0 to satisfy y = g ( x , y ) are a set of recursion relations Ca = P ( D38g ( 0,0 ) , c ) ; Co = 0 ( 3.20 ) = where c1 = Dh ( O ) , | 3 Real Analytic Functions and the Cauchy - Kowalevski Theorem 69.
Página 70
... Analytic and real analytic functions The domain of an analytic function lies in the space C " of vectors x = ( x1 , ... , x ) with n complex components x . For x Є C " , a € Z " we again define x by ( 1.1c ) . We then define analytic ...
... Analytic and real analytic functions The domain of an analytic function lies in the space C " of vectors x = ( x1 , ... , x ) with n complex components x . For x Є C " , a € Z " we again define x by ( 1.1c ) . We then define analytic ...
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