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 ix
Fritz John. ( c ) Duhamel's principle and the general Cauchy problem Problem ( d ) Initial - boundary - value problems ( " Mixed " problems ) Problems 2. Higher - Order Hyperbolic Equations with Constant Coefficients ( a ) Standard form of ...
Fritz John. ( c ) Duhamel's principle and the general Cauchy problem Problem ( d ) Initial - boundary - value problems ( " Mixed " problems ) Problems 2. Higher - Order Hyperbolic Equations with Constant Coefficients ( a ) Standard form of ...
Página 139
... problem with data on a spacelike surface S is established . The argument will not work if S is not spacelike , since ... initial data for t = 0 , and hence vanishes identically . PROBLEM Let S denote a spacelike hyperplane with equation t = ...
... problem with data on a spacelike surface S is established . The argument will not work if S is not spacelike , since ... initial data for t = 0 , and hence vanishes identically . PROBLEM Let S denote a spacelike hyperplane with equation t = ...
Página 247
... initial - value problem 206-215 maximum principle 210 , 215 , 216 mixed problem 220 , 222 non - negative solutions 222-227 regularity 211 , 218-220 , 222 uniqueness 211 , 216 Hilbert space 118 , 190 , 198 representation theorem ...
... initial - value problem 206-215 maximum principle 210 , 215 , 216 mixed problem 220 , 222 non - negative solutions 222-227 regularity 211 , 218-220 , 222 uniqueness 211 , 216 Hilbert space 118 , 190 , 198 representation theorem ...
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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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