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 103
... Maximum Principle * One of the important tools in the theory of harmonic functions is the maximum principle . Similar principles hold for solutions of more general second - order elliptic ... Maximum Principle 103 The Maximum Principle.
... Maximum Principle * One of the important tools in the theory of harmonic functions is the maximum principle . Similar principles hold for solutions of more general second - order elliptic ... Maximum Principle 103 The Maximum Principle.
Página 105
... maximum principle to spherical shell . ] 2. Let u ( x ) = C2 ( N ) Co ( M ) be a solution of n 2 Au + Σ ax ( x ) uxx + c ( x ) u = 0 , k = 1 ( 2.6 ) where c ( x ) < 0 in 2. Show that u = 0 on N implies u = 0 in N. [ Hint : Show that ...
... maximum principle to spherical shell . ] 2. Let u ( x ) = C2 ( N ) Co ( M ) be a solution of n 2 Au + Σ ax ( x ) uxx + c ( x ) u = 0 , k = 1 ( 2.6 ) where c ( x ) < 0 in 2. Show that u = 0 on N implies u = 0 in N. [ Hint : Show that ...
Página 227
... maximum principle , which allows us to work with the maximum norm rather than with L2 - norms . Given two positive constants h , k we again consider the lattice Σ consisting of the points ( x , t ) with x = nh , t = mk 0 < t < T with ...
... maximum principle , which allows us to work with the maximum norm rather than with L2 - norms . Given two positive constants h , k we again consider the lattice Σ consisting of the points ( x , t ) with x = nh , t = mk 0 < t < T with ...
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