Uniqueness of the Solution of a Hyperbolic or Elliptic Differential Equation Problem
Autores
|
4130 |
530,531
|
|
|
5863 |
530,531
|
Informações:
Publicações do PESC
Título
Uniqueness of the Solution of a Hyperbolic or Elliptic Differential Equation Problem
Linha de pesquisa
Otimização
Tipo de publicação
Relatório Técnico
Número de registro
ES-723/8
Data
9/2008
Resumo
Abstract
We consider the problem K ( x ) uxx = utt , 0 g ( t ) E L2 and ux ( 0 , t ) = 0, where K ( x ) is continuous and does not come close to zero. This problem is ill-posed in the sense that, if solution exists, it does not depend continuously on g. We prove that it has at most one solution u ( x , . ) in the Sobolev space H1 ( R ), by assuming that 1 / K ( x ) is Lipschitz.
Arquivo