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 23
... element is called characteristic if it satisfies ( 7.15 ) . A one - parameter family of elements ( x ( t ) , y ( t ) , z ( t ) , p ( t ) , q ( t ) ) is called a strip if the elements are tangent to the curve formed by the points ( x ( t ) ...
... element is called characteristic if it satisfies ( 7.15 ) . A one - parameter family of elements ( x ( t ) , y ( t ) , z ( t ) , p ( t ) , q ( t ) ) is called a strip if the elements are tangent to the curve formed by the points ( x ( t ) ...
Página 24
... element ( xo , Yo - Po , q % ) for z = z 。( in which Po , 9 % are to be replaced by proportional quantities so that F ( xo , Yo , Zo , Po , q0 ) = 0 ( 7.22 ) holds ) . With changing z the line element moves along the curve x = x ( t ) ...
... element ( xo , Yo - Po , q % ) for z = z 。( in which Po , 9 % are to be replaced by proportional quantities so that F ( xo , Yo , Zo , Po , q0 ) = 0 ( 7.22 ) holds ) . With changing z the line element moves along the curve x = x ( t ) ...
Página 118
... element u of S with the Cauchy sequence { u , u , u , ... } in H. We define multiplication by a scalar , addition , and inner product of elements of H by performing these operations for each element of the corresponding Cauchy sequence ...
... element u of S with the Cauchy sequence { u , u , u , ... } in H. We define multiplication by a scalar , addition , and inner product of elements of H by performing these operations for each element of the corresponding Cauchy sequence ...
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