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 ix
Fritz John. ( c ) Duhamel's principle and the general Cauchy problem 135 Problem 139 Problem ( d ) Initial - boundary - value problems ( “ Mixed ” problems ) Problems 2. Higher - Order Hyperbolic Equations with Constant Coefficients ( a ) ...
Fritz John. ( c ) Duhamel's principle and the general Cauchy problem 135 Problem 139 Problem ( d ) Initial - boundary - value problems ( “ Mixed ” problems ) Problems 2. Higher - Order Hyperbolic Equations with Constant Coefficients ( a ) ...
Página 45
... initial - boundary - value problems rather than to “ pure ” initial - value problems . An example is the normal displacement u ( x , t ) of a vibrating string of length 7. Then u satisfies the boundary conditions u ( x , 0 ) = u ( x , π ) ...
... initial - boundary - value problems rather than to “ pure ” initial - value problems . An example is the normal displacement u ( x , t ) of a vibrating string of length 7. Then u satisfies the boundary conditions u ( x , 0 ) = u ( x , π ) ...
Página 247
... initial - value problem 206-215 maximum principle 210 , 215 , 216 mixed problem 220 , 222 non - negative solutions 222-227 regularity 211 , 218-220 , 222 uniqueness 211 , 216 Hilbert space 118 , 190 , 198 representation theorem 118 ...
... initial - value problem 206-215 maximum principle 210 , 215 , 216 mixed problem 220 , 222 non - negative solutions 222-227 regularity 211 , 218-220 , 222 uniqueness 211 , 216 Hilbert space 118 , 190 , 198 representation theorem 118 ...
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