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 10
... contained in S. The tangent to y at P necessarily lies in the tangent plane of S at P. Since the tangent to y has the characteristic direction , the normal to S at P is perpendicular to the characteristic direction , which makes S an ...
... contained in S. The tangent to y at P necessarily lies in the tangent plane of S at P. Since the tangent to y has the characteristic direction , the normal to S at P is perpendicular to the characteristic direction , which makes S an ...
Página 77
... contained in U , and a solution of the Cauchy problem contained in that neighborhood . How far the domain of existence of the Cauchy problem extends in the x - direction depends on the class CM ,, to which the coefficients a ' and b ...
... contained in U , and a solution of the Cauchy problem contained in that neighborhood . How far the domain of existence of the Cauchy problem extends in the x - direction depends on the class CM ,, to which the coefficients a ' and b ...
Página 86
... contained in a given neigh- borhood of Z and the S2 are non - characteristic , since their normals lie close to ... contain two disjoint subsets Z1 and Z2 . It can happen that there exists a domain of determinacy R for Z1 that contains ...
... contained in a given neigh- borhood of Z and the S2 are non - characteristic , since their normals lie close to ... contain two disjoint subsets Z1 and Z2 . It can happen that there exists a domain of determinacy R for Z1 that contains ...
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