The Hardy inequality and the asymptotic behaviour
of the heat equation in twisted waveguides.
David Krejcirik,
(Instituto BCAM)
Jueves 18 de noviembre de 2010
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 the existence of Hardy inequalities
for the Dirichlet Laplacian in twisted tubes
and the method of self-similar variables
and weighted Sobolev spaces for the heat equation.
This is a joint work with Enrique Zuazua.