Heat equation with singular thermal conductivity
Analysis of PDEs
2023-02-21 v1
Abstract
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the classical solution if the latter exists are shown. Indeed, we allow the coefficient to be a distribution with a toy example of a Delta-function.
Keywords
Cite
@article{arxiv.2302.09314,
title = {Heat equation with singular thermal conductivity},
author = {Michael Ruzhansky and Mohammed Elamine Sebih and Niyaz Tokmagambetov},
journal= {arXiv preprint arXiv:2302.09314},
year = {2023}
}