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 54
Página 102
... Prove that Au ( x ) = △ u ( x1 , ... , Xn ) = 0 also implies that △ ( | x | 2 ̄ " u ( x / | x | 2 ) ) = 0 for x / x2 in the domain of definition of u . ( 1.38 ) 6. Let x , y denote coordinates in the plane . Let u ( x , y ) be a ...
... Prove that Au ( x ) = △ u ( x1 , ... , Xn ) = 0 also implies that △ ( | x | 2 ̄ " u ( x / | x | 2 ) ) = 0 for x / x2 in the domain of definition of u . ( 1.38 ) 6. Let x , y denote coordinates in the plane . Let u ( x , y ) be a ...
Página 103
Fritz John. ( a ) Prove that F = gradu , where the " potential " u is given by u ( § ) Y μ ( χ ) u ( E ) = x S S S x ( x ) dx . | x § | ( b ) Prove that the attraction F ( § ) exerted by N on a far away unit mass is approximately the ...
Fritz John. ( a ) Prove that F = gradu , where the " potential " u is given by u ( § ) Y μ ( χ ) u ( E ) = x S S S x ( x ) dx . | x § | ( b ) Prove that the attraction F ( § ) exerted by N on a far away unit mass is approximately the ...
Página 125
... prove that the w * form a Cauchy sequence converging to an element w of H with ( w ) = 1 , wm . Show that ( w , u ) = 0 for ( u ) = 0 , and finally that ( v , u ) = 4 ( u ) for v = w / ( w , w ) and all u . ] 2. Show that a solution ...
... prove that the w * form a Cauchy sequence converging to an element w of H with ( w ) = 1 , wm . Show that ( w , u ) = 0 for ( u ) = 0 , and finally that ( v , u ) = 4 ( u ) for v = w / ( w , w ) and all u . ] 2. Show that a solution ...
Contenido
Chapter | 1 |
Examples | 2 |
Analytic Solution and Approximation Methods in a Simple Example Problems 4 Quasilinear Equations | 4 |
Derechos de autor | |
Otras 35 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
analytic functions assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f fundamental solution Gårding Gårding's inequality given harmonic function heat equation hence Hint Ho(N holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix maximum principle neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof real analytic real numbers satisfies scalar Show solution u(x,t solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ