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. |
Dentro del libro
Resultados 1-3 de 92
Página vii
... Linear and Quasi - linear Second - order Equations 2. Propagation of Singularities 3. The Linear Second - Order Equation Problems 4. The One - Dimensional Wave Equation Problems 1 12 2 4 8 9 11 15 18 2225 19 24 29 31 33 * 3w www 33 35 ...
... Linear and Quasi - linear Second - order Equations 2. Propagation of Singularities 3. The Linear Second - Order Equation Problems 4. The One - Dimensional Wave Equation Problems 1 12 2 4 8 9 11 15 18 2225 19 24 29 31 33 * 3w www 33 35 ...
Página 37
... , y ) , ( 3.2 ) we transform this linear equation into one of the same type , Lu = A ( § , n ) uε + 2B ( §‚n ) u ̧n + ··· = 0 , 23 ( 3.3 ) where , A = aq2 + 2box & , + 3 The Linear Second - Order Equation 37 The Linear Second-Order Equation.
... , y ) , ( 3.2 ) we transform this linear equation into one of the same type , Lu = A ( § , n ) uε + 2B ( §‚n ) u ̧n + ··· = 0 , 23 ( 3.3 ) where , A = aq2 + 2box & , + 3 The Linear Second - Order Equation 37 The Linear Second-Order Equation.
Página 235
... linear partial differential equations always have solutions , in fact so many that it is possible to impose ... linear equation without sin- gular points that has no solution anywhere . His equation has the form Lu = F where the linear ...
... linear partial differential equations always have solutions , in fact so many that it is possible to impose ... linear equation without sin- gular points that has no solution anywhere . His equation has the form Lu = F where the linear ...
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