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 38
... transformation , x ' = έ + n , y ' = έ — n , one can also transform ( 3.5 ) into the alternate form ulic mur- Uy'y ' — Ux'x ' + 2D'ux + 2E'u + F'u = 0 . ( 3.6 ) ( 3.7 ) In the elliptic case , where ac - b2 > 0 , there exist no real ...
... transformation , x ' = έ + n , y ' = έ — n , one can also transform ( 3.5 ) into the alternate form ulic mur- Uy'y ' — Ux'x ' + 2D'ux + 2E'u + F'u = 0 . ( 3.6 ) ( 3.7 ) In the elliptic case , where ac - b2 > 0 , there exist no real ...
Página 145
... transformation † Following Cauchy a formal solution of the standard problem ( 2.14a , b , c ) can be obtained by Fourier transformation with respect to the space * Using the finiteness of the domain of dependence of u on g ( implied ...
... transformation † Following Cauchy a formal solution of the standard problem ( 2.14a , b , c ) can be obtained by Fourier transformation with respect to the space * Using the finiteness of the domain of dependence of u on g ( implied ...
Página 157
... transformation In many cases mixed initial - boundary - value problems can be solved by Fourier transformation , when the domain of the solution is a half space . The method will be illustrated ( following R. Hersh * ) by a problem for ...
... transformation In many cases mixed initial - boundary - value problems can be solved by Fourier transformation , when the domain of the solution is a half space . The method will be illustrated ( following R. Hersh * ) by a problem 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