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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... integral surface . Conversely we can show that every integral surface S is the union of characteristic curves , or that through every point of S there passes a characteristic curve contained in S. This is a consequence of the following ...
... integral surface . Conversely we can show that every integral surface S is the union of characteristic curves , or that through every point of S there passes a characteristic curve contained in S. This is a consequence of the following ...
Página 20
... integral surface at that point , described by the direction numbers P , q , - 1. An integral surface passing through a given point Po = ( xo , Yo , Zo ) must have a tangent plane z - zo = p ( x - xo ) + q ( y − yo ) - for which the ...
... integral surface at that point , described by the direction numbers P , q , - 1. An integral surface passing through a given point Po = ( xo , Yo , Zo ) must have a tangent plane z - zo = p ( x - xo ) + q ( y − yo ) - for which the ...
Página 30
... integral surface of ( 7.1 ) passing through a curve I can be solved directly with a knowledge of the two - parameter family ( 9.4 ) . We only have to find a one - parameter sub- family of integral surfaces that touch г and then form ...
... integral surface of ( 7.1 ) passing through a curve I can be solved directly with a knowledge of the two - parameter family ( 9.4 ) . We only have to find a one - parameter sub- family of integral surfaces that touch г and then form ...
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