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 28
Página 20
... normal of the integral surface at that point , described by the direction numbers p , q , - 1. An integral surface passing through a given point P 。= ( xo , Yo , Zo ) must have a tangent plane z - zo = p ( x − xo ) + q ( y − yo ) for ...
... normal of the integral surface at that point , described by the direction numbers p , q , - 1. An integral surface passing through a given point P 。= ( xo , Yo , Zo ) must have a tangent plane z - zo = p ( x − xo ) + q ( y − yo ) for ...
Página 29
... normal to the level line y ,. We see that the wave fronts y , form a family of curves with common normals ( " parallel " curves ) . Here y , can also be obtained from yo by laying off a fixed distance ct along each normal of Yo . Thus y ...
... normal to the level line y ,. We see that the wave fronts y , form a family of curves with common normals ( " parallel " curves ) . Here y , can also be obtained from yo by laying off a fixed distance ct along each normal of Yo . Thus y ...
Página 57
... normal derivatives of order less than m can be given independently from each other ) . We are to find a solution u near S which has these Cauchy data on S. We call S noncharacteristic if we can get all Du for | a | = m on S from the ...
... normal derivatives of order less than m can be given independently from each other ) . We are to find a solution u near S which has these Cauchy data on S. We call S noncharacteristic if we can get all Du for | a | = m on S from the ...
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