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 77
Página 11
... Cauchy Problem for the Quasi - linear Equation We now have a simple description for the general solution u of ( 4.2 ) : The integral surface z = u ( x , y ) is the union of characteristic ... Cauchy Problem for the Quasi - linear Equation 11.
... Cauchy Problem for the Quasi - linear Equation We now have a simple description for the general solution u of ( 4.2 ) : The integral surface z = u ( x , y ) is the union of characteristic ... Cauchy Problem for the Quasi - linear Equation 11.
Página 13
... Cauchy problem , under the assumption ( 5.14 ) . Uniqueness follows from the theo- rem on p . 10 : Any integral surface through I would have to contain the ... Cauchy Problem for the Quasi - linear Equation 13 The Cauchy Problem.
... Cauchy problem , under the assumption ( 5.14 ) . Uniqueness follows from the theo- rem on p . 10 : Any integral surface through I would have to contain the ... Cauchy Problem for the Quasi - linear Equation 13 The Cauchy Problem.
Página 76
... Cauchy problems . It does not guarantee global existence of solutions ; it does not exclude the possibility that other non - analytic solutions exist for the same Cauchy problem 76 3 Characteristic Manifolds and the Cauchy Problem.
... Cauchy problems . It does not guarantee global existence of solutions ; it does not exclude the possibility that other non - analytic solutions exist for the same Cauchy problem 76 3 Characteristic Manifolds and the Cauchy Problem.
Contenido
Chapter | 1 |
Examples | 2 |
Analytic Solution and Approximation Methods in a Simple Example Problems 4 Quasilinear Equations | 4 |
Derechos de autor | |
Otras 35 secciones no mostradas
Otras ediciones - Ver todas
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