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 45
... solution u ( x , t ) of ( 4.1 ) in the quadrant u = f ( x ) , = u = g ( x ) for t = 0 , x > 0 u , aux for x = 0,1 > 0 , where ƒ and g are of class C2 for x > 0 and vanish near x = 0 . ( Hint : Use ( 4.5 ) ) . Show that generally no solution ...
... solution u ( x , t ) of ( 4.1 ) in the quadrant u = f ( x ) , = u = g ( x ) for t = 0 , x > 0 u , aux for x = 0,1 > 0 , where ƒ and g are of class C2 for x > 0 and vanish near x = 0 . ( Hint : Use ( 4.5 ) ) . Show that generally no solution ...
Página 77
... solutions is unrealistic . It implies that the solution is determined globally by local conditions near one point , and makes it impossible to describe phenomena that do not interact instantaneously with the whole universe ( hence it ...
... solutions is unrealistic . It implies that the solution is determined globally by local conditions near one point , and makes it impossible to describe phenomena that do not interact instantaneously with the whole universe ( hence it ...
Página 145
... solution Из of a standard problem corresponds to the data ( 2.5 ) . For a nonchar- acteristic initial plane t = 0 the matrix P ( 0 , 1 ) is nondegenerate , and we can assume that P ( 0,1 ) = 1 ( 2.12 ) is the unit matrix . The solution ...
... solution Из of a standard problem corresponds to the data ( 2.5 ) . For a nonchar- acteristic initial plane t = 0 the matrix P ( 0 , 1 ) is nondegenerate , and we can assume that P ( 0,1 ) = 1 ( 2.12 ) is the unit matrix . The solution ...
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