Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Analysis of PDEs
2026-04-28 v1
Abstract
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may not exist in this setting, we employ the framework of very weak solutions to establish the existence and uniqueness of solutions to the heat equation with singular, anisotropic, time-dependent diffusivity.
Keywords
Cite
@article{arxiv.2604.23856,
title = {Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity},
author = {Zhirayr Avetisyan and Zahra Keyshams and Monire Mikaeili Nia and Michael Ruzhansky},
journal= {arXiv preprint arXiv:2604.23856},
year = {2026}
}
Comments
This is a preliminary version of the work