The Hardy inequality and the heat equation in twisted tubes

We show that a twist of a three-dimensional tube of uniform cross-section yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for the Dirichlet Laplacian in twisted tubes and the method of self-similar variabl...

ver descrição completa

Detalhes bibliográficos
Autores: Krejčiřík, D., Zuazua, E.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/486
Acesso em linha:http://hdl.handle.net/20.500.11824/486
Access Level:acceso abierto
Palavra-chave:Dirichlet Laplacian
Hardy inequality
Heat equation
Large time behaviour of solutions
Twisted tubes
Descrição
Resumo:We show that a twist of a three-dimensional tube of uniform cross-section yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for the Dirichlet Laplacian in twisted tubes and the method of self-similar variables and weighted Sobolev spaces for the heat equation. © 2010 Elsevier Masson SAS.