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 173
... difference operators 80,8 ; by E - 1 & = for j = 1 , ... , n h 80 = E0-1 Eo k so that , for example , u ( x , t + k ) −u ( x , t ) δου ( x , t ) = k ( 3.29d ) ( 3.30a ) ( 3.30b ) The operators Ej , Еk , dj , & commute . For functions ...
... difference operators 80,8 ; by E - 1 & = for j = 1 , ... , n h 80 = E0-1 Eo k so that , for example , u ( x , t + k ) −u ( x , t ) δου ( x , t ) = k ( 3.29d ) ( 3.30a ) ( 3.30b ) The operators Ej , Еk , dj , & commute . For functions ...
Página 231
... difference quotients of v . Let w ( x , t ) be defined in Σ by v ( x + h , t ) −v ( x , t ) w = dv = 1 ( E – 1 ) v h Using the product rule ( 2.22 ) ( 2.23 ) 8 ( ab ) = ( Ea ) 8b + ( da ) b , we find from ( 2.6 ) that w satisfies the ...
... difference quotients of v . Let w ( x , t ) be defined in Σ by v ( x + h , t ) −v ( x , t ) w = dv = 1 ( E – 1 ) v h Using the product rule ( 2.22 ) ( 2.23 ) 8 ( ab ) = ( Ea ) 8b + ( da ) b , we find from ( 2.6 ) that w satisfies the ...
Página 246
... Difference equation 5 stability 7 , 174 Difference operator 173 Difference quotient backward 7 central 174 Dirac function 90 , 199 Dirichlet data 140 integral 119 , 125 norm 120 , 121 principle 125 Dirichlet problem 95 , 103 , 106 , 111 ...
... Difference equation 5 stability 7 , 174 Difference operator 173 Difference quotient backward 7 central 174 Dirac function 90 , 199 Dirichlet data 140 integral 119 , 125 norm 120 , 121 principle 125 Dirichlet problem 95 , 103 , 106 , 111 ...
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