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 47
... assumed to be non - characteristic : u ( x , 0 ) = f ( x ) , det A0 for t = 0 . For small t we can then solve for u , in ( 5.5 ) getting a new equation u , + B ( x , t ) u ... assume the system ( 5.5 ) 5 Systems of First - Order Equations 47.
... assumed to be non - characteristic : u ( x , 0 ) = f ( x ) , det A0 for t = 0 . For small t we can then solve for u , in ( 5.5 ) getting a new equation u , + B ( x , t ) u ... assume the system ( 5.5 ) 5 Systems of First - Order Equations 47.
Página 103
... assumes its maximum certainly on the boundary of , possibly also in N. ) Indeed under the stronger assumption Au > 0 in 2 , relation ( 2.1 ) follows from the fact that u cannot assume its maximum at any point έEN ; for * ( [ 28 ] ) then ...
... assumes its maximum certainly on the boundary of , possibly also in N. ) Indeed under the stronger assumption Au > 0 in 2 , relation ( 2.1 ) follows from the fact that u cannot assume its maximum at any point έEN ; for * ( [ 28 ] ) then ...
Página 152
... Assume Imμy < 0 ( otherwise replace n by -n and μo by - ) . Then there exist roots μ of ( 2.42 ) for all sufficiently large p for which Imμ < -y / 2 and hence roots of ( 2.29 ) for which Im 2 < −py / 2 . This contradicts ( 2.30 ) for ...
... Assume Imμy < 0 ( otherwise replace n by -n and μo by - ) . Then there exist roots μ of ( 2.42 ) for all sufficiently large p for which Imμ < -y / 2 and hence roots of ( 2.29 ) for which Im 2 < −py / 2 . This contradicts ( 2.30 ) for ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
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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