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 34
... Cauchy data uniquely determine the second derivatives of u on y . As a matter of fact , we can then also find ... Cauchy problem in terms of powers of x - xo , y - yo . It would be an actual representation of the solution u in a ...
... Cauchy data uniquely determine the second derivatives of u on y . As a matter of fact , we can then also find ... Cauchy problem in terms of powers of x - xo , y - yo . It would be an actual representation of the solution u in a ...
Página 57
... Cauchy data on S. We call S noncharacteristic if we can get all Du for | a | = m on S from the linear algebraic system of equations consisting of the compatibility conditions for the data and the partial differential equation ( 2.2 ) ...
... Cauchy data on S. We call S noncharacteristic if we can get all Du for | a | = m on S from the linear algebraic system of equations consisting of the compatibility conditions for the data and the partial differential equation ( 2.2 ) ...
Página 77
... data to belong to some class C3 or even to C , instead of C. * Many physical problems lead to analytic partial differential equations . But the restriction to analytic Cauchy data and solutions is unrealistic . It implies that the ...
... data to belong to some class C3 or even to C , instead of C. * Many physical problems lead to analytic partial differential equations . But the restriction to analytic Cauchy data and solutions is unrealistic . It implies that the ...
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