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. |
Dentro del libro
Resultados 1-3 de 91
Página vii
... Linear and Quasi - linear Second - order Equations 2. Propagation of Singularities 3 . The Linear Second - Order Equation Problems 4. The One - Dimensional Wave Equation Problems 335 33 * 3 www w 35 37 39 40 45 5. Systems of First ...
... Linear and Quasi - linear Second - order Equations 2. Propagation of Singularities 3 . The Linear Second - Order Equation Problems 4. The One - Dimensional Wave Equation Problems 335 33 * 3 www w 35 37 39 40 45 5. Systems of First ...
Página 37
... , y ) , ( 3.2 ) we transform this linear equation into one of the same type , Lu = A ( § , n ) ugε + 2B ( § , n ) u ̧n + ··· = 0 , ( 3.3 ) where , A = a & 2 + 2box , 3 The Linear Second - Order Equation 37 The Linear Second-Order Equation.
... , y ) , ( 3.2 ) we transform this linear equation into one of the same type , Lu = A ( § , n ) ugε + 2B ( § , n ) u ̧n + ··· = 0 , ( 3.3 ) where , A = a & 2 + 2box , 3 The Linear Second - Order Equation 37 The Linear Second-Order Equation.
Página 235
... linear equation without sin- gular points that has no solution anywhere . His equation has the form Lu F where the linear first order differential operator L has complex- valued linear functions as coefficients , and F is a suitably ...
... linear equation without sin- gular points that has no solution anywhere . His equation has the form Lu F where the linear first order differential operator L has complex- valued linear functions as coefficients , and F is a suitably ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
Otras 20 secciones no mostradas
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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