Removability of time-dependent singularities in the heat equation
Analysis of PDEs
2013-07-12 v2
Abstract
We consider solutions of the linear heat equation with time-dependent singularities. It is shown that if a singularity is weaker than the order of the fundamental solution of the Laplace equation, then it is removable. We also consider the removability of higher dimensional singular sets. An example of a non-removable singularity is given, which implies the optimality of the condition for removability.
Keywords
Cite
@article{arxiv.1304.5147,
title = {Removability of time-dependent singularities in the heat equation},
author = {Jin Takahashi and Eiji Yanagida},
journal= {arXiv preprint arXiv:1304.5147},
year = {2013}
}
Comments
19 pages