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.

中文翻译：

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剪切无界带中热方程的渐近行为

我们表明，剪切的几何变形为无界带中与狄利克雷拉普拉斯算子相关的热半群产生了改进的衰减率。证明是基于由 [2] 中建立的剪切引起的 Hardy 不等式以及热方程的自相似变量和加权 Sobolev 空间的方法。