Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia, Michael Ruzhansky
DOI: 10.48550/arxiv.2604.23856
Cited by: 0

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.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Navier-Stokes equation solutions Geometric Analysis and Curvature Flows

Publication details

Journal / source
arXiv (Cornell University)
Publication date
26 April 2026
Language
EN
Document type
Preprint