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 16
... origin . More precisely the only solution u of ( 6.5 ) of class C1 in a neighborhood of the origin is u = 0 . For along any ray x1 = c ; t i = 1 , ... , n from the origin referred to a parameter t we have by ( 6.5 ) t M = + froust ! rut ...
... origin . More precisely the only solution u of ( 6.5 ) of class C1 in a neighborhood of the origin is u = 0 . For along any ray x1 = c ; t i = 1 , ... , n from the origin referred to a parameter t we have by ( 6.5 ) t M = + froust ! rut ...
Página 74
... origin and S locally by an analytic transformation into a neighborhood of the origin in the plane Xn x = 0. Then by introducing derivatives of orders less than m as new depen- dent variables one reduces the system to one of first order ...
... origin and S locally by an analytic transformation into a neighborhood of the origin in the plane Xn x = 0. Then by introducing derivatives of orders less than m as new depen- dent variables one reduces the system to one of first order ...
Página 78
... origin in their arguments . Show directly , by the method of majorants ( without reduction to the quasi - linear case ) , that this Cauchy problem has a solution which is real analytic at the origin . 4. Let u ( x1 , x2 ) denote a ...
... origin in their arguments . Show directly , by the method of majorants ( without reduction to the quasi - linear case ) , that this Cauchy problem has a solution which is real analytic at the origin . 4. Let u ( x1 , x2 ) denote a ...
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