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 38
... hyperbolic case , that one can simplify the differential equation by introducing the characteristics as new coordinate lines . Let = ( x , y ) = const . , n = ( x , y ) = const . be the two families of characteristics in the xy - plane ...
... hyperbolic case , that one can simplify the differential equation by introducing the characteristics as new coordinate lines . Let = ( x , y ) = const . , n = ( x , y ) = const . be the two families of characteristics in the xy - plane ...
Página 143
... Hyperbolic Equations with Constant Coefficients ( a ) Standard form of the initial - value problem For functions u ... Hyperbolic Equations with Constant Coefficients 143 Higher-Order Hyperbolic Equations with Constant Coefficients (a) ...
... Hyperbolic Equations with Constant Coefficients ( a ) Standard form of the initial - value problem For functions u ... Hyperbolic Equations with Constant Coefficients 143 Higher-Order Hyperbolic Equations with Constant Coefficients (a) ...
Página 152
... hyperbolic when its principal part Pm ( § , λ ) = 0 has real distinct roots for $ 0 hyperbolic . We see that strict hyperbolicity implies hyperbolicity . Thus , for example , any equation of the form is hyperbolic . utt = c2 △ u + ku ...
... hyperbolic when its principal part Pm ( § , λ ) = 0 has real distinct roots for $ 0 hyperbolic . We see that strict hyperbolicity implies hyperbolicity . Thus , for example , any equation of the form is hyperbolic . utt = c2 △ u + ku ...
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