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 48
... components vi , c = ( cik ) , and d has components d , we find from ( 5.17 ) , along a characteristic C ; of the ith family , do მა მა ; dvdv ; + dx dvd ; + 1 = Σ Cik Uk + d1 . = = dt Ət dt ax Ət λi əx ( 5.19 ) The ith backward ...
... components vi , c = ( cik ) , and d has components d , we find from ( 5.17 ) , along a characteristic C ; of the ith family , do მა მა ; dvdv ; + dx dvd ; + 1 = Σ Cik Uk + d1 . = = dt Ət dt ax Ət λi əx ( 5.19 ) The ith backward ...
Página 54
... components are non - negative integers a are called multi - indices and form a subset Z " of R " . Letters x , y ... Components are always indicated by adding a subscript to the vector symbol : has components . In R " we introduce the ...
... components are non - negative integers a are called multi - indices and form a subset Z " of R " . Letters x , y ... Components are always indicated by adding a subscript to the vector symbol : has components . In R " we introduce the ...
Página 59
... components ( 0 , ... , 0,1 ) . But then = Cŋ is just the column vector with components dy / dx ; = D1o , that is , the vector Do. Thus , the condition for noncharacteristic behavior of S can again be written as ( 2.13 ) . If u in ( 2.2 ) ...
... components ( 0 , ... , 0,1 ) . But then = Cŋ is just the column vector with components dy / dx ; = D1o , that is , the vector Do. Thus , the condition for noncharacteristic behavior of S can again be written as ( 2.13 ) . If u in ( 2.2 ) ...
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