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 6
... consists of the set of points x , x + h , x + 2h , x + nh ... 9 - ( 3.10 ) on the x - axis , all of which lie between x and x + nh . The domain of the differential equation solution consists of the point = x - ct = x − cλnh , which ...
... consists of the set of points x , x + h , x + 2h , x + nh ... 9 - ( 3.10 ) on the x - axis , all of which lie between x and x + nh . The domain of the differential equation solution consists of the point = x - ct = x − cλnh , which ...
Página 23
... consisting of a two - parameter family of elements ( x ( s , t ) , y ( s , t ) , z ( s , t ) , p ( s , t ) , q ( s ... consists of a point P of an integral surface S and of the tangent plane to S at P , then the strip is made up of the ...
... consisting of a two - parameter family of elements ( x ( s , t ) , y ( s , t ) , z ( s , t ) , p ( s , t ) , q ( s ... consists of a point P of an integral surface S and of the tangent plane to S at P , then the strip is made up of the ...
Página 24
... consisting of the point ( x , y ) and the line 0 = p ( § − x ) + q ( n − y ) ( 7.20 ) in running coordinates $ , n ... consists in passing an integral surface through an " arbitrary ” initial curve I given parametrically in the form x ...
... consisting of the point ( x , y ) and the line 0 = p ( § − x ) + q ( n − y ) ( 7.20 ) in running coordinates $ , n ... consists in passing an integral surface through an " arbitrary ” initial curve I given parametrically in the form x ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
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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