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 51
Página 4
... example of a third - order nonlinear equation for a function u ( x , t ) is furnished by the Korteweg - de Vries equation u1 + cuux + uxxx = 0 first encountered in the study of water waves . ( 2.17 ) In general we shall try to describe ...
... example of a third - order nonlinear equation for a function u ( x , t ) is furnished by the Korteweg - de Vries equation u1 + cuux + uxxx = 0 first encountered in the study of water waves . ( 2.17 ) In general we shall try to describe ...
Página 91
... example we have from ( 6.9 ) that DÂd [ 4 ] = − ( § ) . In particular , ( 6.13 ) yields a definition for derivatives of a continuous func- tion f ( x ) , not necessarily as a function with point values , but as a generalized function ...
... example we have from ( 6.9 ) that DÂd [ 4 ] = − ( § ) . In particular , ( 6.13 ) yields a definition for derivatives of a continuous func- tion f ( x ) , not necessarily as a function with point values , but as a generalized function ...
Página 235
... example is not given explicitly ; its existence is proved by a non - constructive argument . The single equation Lu = F with complex coefficients for a complex - valued u is equivalent to a system of two equations with real coefficients ...
... example is not given explicitly ; its existence is proved by a non - constructive argument . The single equation Lu = F with complex coefficients for a complex - valued u is equivalent to a system of two equations with real coefficients ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
Otras 20 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Cauchy-Kowalevski Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders determined uniquely difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f(x fundamental solution Gårding given Green's identity heat equation hence Hint holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof quasi-linear real numbers satisfies scalar second derivatives Show solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ