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 23
... plane through the point with equation 3 − z = p ( § − x ) + q ( n − y ) ( 7.16 ) in running coordinates § , n ,. Then p , q , -1 are direction numbers of the normal of the plane . An element is called characteristic if it satisfies ...
... plane through the point with equation 3 − z = p ( § − x ) + q ( n − y ) ( 7.16 ) in running coordinates § , n ,. Then p , q , -1 are direction numbers of the normal of the plane . An element is called characteristic if it satisfies ...
Página 88
... plane x , 0. Let y be a point of R " with yn > 0 , and let R be the cone with vertex y and base Z ( that is , R is the union of the closed line segments joining y to a point of Z ) . Let every plane of support of R at y ( that is ...
... plane x , 0. Let y be a point of R " with yn > 0 , and let R be the cone with vertex y and base Z ( that is , R is the union of the closed line segments joining y to a point of Z ) . Let every plane of support of R at y ( that is ...
Página 159
... plane waves can be preferable , since it does not involve the somewhat artificial introduction of exponentials . A function G with domain R " is called a plane wave function , if its level surfaces form a family of parallel planes ...
... plane waves can be preferable , since it does not involve the somewhat artificial introduction of exponentials . A function G with domain R " is called a plane wave function , if its level surfaces form a family of parallel planes ...
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