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 20
Página 98
... class C2 in any closed ball contained in 2 and hence real analytic in the open ball . Thus harmonic functions are real analytic in the interior of their domain of definition . ∞ We can conclude from this that the Cauchy problem for the ...
... class C2 in any closed ball contained in 2 and hence real analytic in the open ball . Thus harmonic functions are real analytic in the interior of their domain of definition . ∞ We can conclude from this that the Cauchy problem for the ...
Página 129
... class C2 for t > 0 in n = 3 space dimensions is given by formula ( 1.14 ) , hence is unique . Conversely for any ƒ E C3 ( R3 ) and gЄ C2 ( R3 ) the u ( x , t ) defined by ( 1.14 ) is of class C2 and satisfies ( 1.1 ) , ( 1.2 ) . Indeed ...
... class C2 for t > 0 in n = 3 space dimensions is given by formula ( 1.14 ) , hence is unique . Conversely for any ƒ E C3 ( R3 ) and gЄ C2 ( R3 ) the u ( x , t ) defined by ( 1.14 ) is of class C2 and satisfies ( 1.1 ) , ( 1.2 ) . Indeed ...
Página 203
... C2 . Then ( see the defini- tion in problem 9 , p . 198 ) there exists a 1 - 1 mapping x = F ( y ) of class C2 with non - vanishing Jacobian and inverse y = f ( x ) , which maps 0 onto x1 , the ball y < 1 onto a neighborhood w of x1 and ...
... C2 . Then ( see the defini- tion in problem 9 , p . 198 ) there exists a 1 - 1 mapping x = F ( y ) of class C2 with non - vanishing Jacobian and inverse y = f ( x ) , which maps 0 onto x1 , the ball y < 1 onto a neighborhood w of x1 and ...
Contenido
Chapter | 1 |
Examples | 2 |
Analytic Solution and Approximation Methods in a Simple Example Problems 4 Quasilinear Equations | 4 |
Derechos de autor | |
Otras 35 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
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