The asymptotic behaviour of the heat equation in a sheared unbounded strip

[摘要] We show that the geometric deformation of shearing yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in an unbounded strip. The proof is based on the Hardy inequality due to the shearing established in [2] and the method of self-similar variables and weighted Sobolev spaces for the heat equation. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-05

[关键词] Dirichlet Laplacian;Hardy inequality;Subcriticality;Heat equation;Large-time behaviour of solutions;Sheared strip