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. |
Dentro del libro
Resultados 1-3 de 37
Página 50
... positive eigenvalues of the matrix B. Let , say , the number r be such that λ , > λ2 ... > λ , > 0 > λ , + 1 > ... > λn . ( 5.31 ) The characteristics C ; of the ith family then have positive slopes for i = 1 , ... , r , negative ones ...
... positive eigenvalues of the matrix B. Let , say , the number r be such that λ , > λ2 ... > λ , > 0 > λ , + 1 > ... > λn . ( 5.31 ) The characteristics C ; of the ith family then have positive slopes for i = 1 , ... , r , negative ones ...
Página 65
... positive numbers M , r such that for all x E N 1 f ( x ) = Σ Σ ~ ( Daf ( y ) ) ( x − y ) a ( D * f ( y ) ) ( x – y ) a ! α \ D®ƒx ( x ) | ≤ M | B | ! r - 1B for all ẞ € Z " ( 3.9a ) and all k . ( 3.9b ) Real analytic fenjoy the ...
... positive numbers M , r such that for all x E N 1 f ( x ) = Σ Σ ~ ( Daf ( y ) ) ( x − y ) a ( D * f ( y ) ) ( x – y ) a ! α \ D®ƒx ( x ) | ≤ M | B | ! r - 1B for all ẞ € Z " ( 3.9a ) and all k . ( 3.9b ) Real analytic fenjoy the ...
Página 171
... positive definite for all ( x , t ) on S1 . Let A , A1 , ... , A " be symmetric , A positive definite , and R1 be space - like . Let u e C1 ( R ) be a solution of Set Lu = W for ( x , t ) = R2 ( 3.27d ) u = f ( x ) for t = 0 , | x ...
... positive definite for all ( x , t ) on S1 . Let A , A1 , ... , A " be symmetric , A positive definite , and R1 be space - like . Let u e C1 ( R ) be a solution of Set Lu = W for ( x , t ) = R2 ( 3.27d ) u = f ( x ) for t = 0 , | x ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
Otras 20 secciones no mostradas
Otras ediciones - Ver todas
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