Edge Singular Behavior for the Heat Equation on Polyhedral Cylinders in $\boldsymbol{\mathbb{R}}^{\bf 3}$

Abstract

We study the Heat equation in the polyhedral cylinder with a non-convex edge. We construct the singularity functions depending on the time and edge axis, and the coefficient of the singularity, called the stress intensity distributions, and show regularity results for the solution and the coefficient. The regularity is achieved in the (not weighted) Sobolev space in the L2 and Lq spaces, respectively. An application to the finite polyhedral cylinder is described.