English

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}
}
R2 v1 2026-06-28T08:43:26.719Z