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 29
... obtain the " general " solution of ( 7.1 ) and the " general " characteristic strip from any special two - parameter family u = G ( x , y , λ , μ ) ( 9.4 ) of solutions of ( 7.1 ) . Many different one - parameter families are obtained ...
... obtain the " general " solution of ( 7.1 ) and the " general " characteristic strip from any special two - parameter family u = G ( x , y , λ , μ ) ( 9.4 ) of solutions of ( 7.1 ) . Many different one - parameter families are obtained ...
Página 30
... obtain an integral surface with a conical singularity at ( xo , yo , Zo ) , called the " conoid " solution . The solution of the general Cauchy problem can be obtained by taking the envelope of the conoids that have their singularities ...
... obtain an integral surface with a conical singularity at ( xo , yo , Zo ) , called the " conoid " solution . The solution of the general Cauchy problem can be obtained by taking the envelope of the conoids that have their singularities ...
Página 75
... obtain by applying D and setting x = 0 relations of the form D „ Du ̧ ( 0 ) = P ( d3aƒx ( 0 ) , d3⁄4b¡ ( 0 ) , D3μ¿ ( 0 ) ... obtained from 3.32a , e ) , converge near x = 0 . This is easily achieved by the method of majorants . Let aj ( z ) ...
... obtain by applying D and setting x = 0 relations of the form D „ Du ̧ ( 0 ) = P ( d3aƒx ( 0 ) , d3⁄4b¡ ( 0 ) , D3μ¿ ( 0 ) ... obtained from 3.32a , e ) , converge near x = 0 . This is easily achieved by the method of majorants . Let aj ( z ) ...
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