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Main Authors: Avetisyan, Zhirayr, Keyshams, Zahra, Nia, Monire Mikaeili, Ruzhansky, Michael
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.23856
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author Avetisyan, Zhirayr
Keyshams, Zahra
Nia, Monire Mikaeili
Ruzhansky, Michael
author_facet Avetisyan, Zhirayr
Keyshams, Zahra
Nia, Monire Mikaeili
Ruzhansky, Michael
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_23856
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Avetisyan, Zhirayr
Keyshams, Zahra
Nia, Monire Mikaeili
Ruzhansky, Michael
Analysis of PDEs
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.
title Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
topic Analysis of PDEs
url https://arxiv.org/abs/2604.23856