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 35
... regions of the plane . 2. Propagation of Singularities The characteristic curves are closely associated with the ... region in the xy - plane divided by a curve y into two portions I and II . There shall be two solutions ul and ull ...
... regions of the plane . 2. Propagation of Singularities The characteristic curves are closely associated with the ... region in the xy - plane divided by a curve y into two portions I and II . There shall be two solutions ul and ull ...
Página 43
... regions by the characteristics through the corners and through the points of intersections of the characteristics ... region II we form the characteris- tic parallelogram with vertices A , B , C , D and get u ( A ) from ( 4.15 ) as u ...
... regions by the characteristics through the corners and through the points of intersections of the characteristics ... region II we form the characteris- tic parallelogram with vertices A , B , C , D and get u ( A ) from ( 4.15 ) as u ...
Página 106
... region x2 + ( x2 + 1 ) 2 < a2 , x2 > 0 with large a . Let ε → 0 . ] 3. The Dirichlet Problem , Green's Function , and Poisson's Formula We derived the representation ( 1.23 ) for u in terms of Cauchy data , involving a fundamental ...
... region x2 + ( x2 + 1 ) 2 < a2 , x2 > 0 with large a . Let ε → 0 . ] 3. The Dirichlet Problem , Green's Function , and Poisson's Formula We derived the representation ( 1.23 ) for u in terms of Cauchy data , involving a fundamental ...
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