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

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.

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Publication Details

Journal
ArXiv.org
Published
2025-07-18
Primary Topic
Nonlinear Partial Differential Equations
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article
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article

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

Michael Ruzhansky, Zahra Keyshams, Zhirayr Avetisyan, Monire Mikaeili Nia
ArXiv.org
Nonlinear Partial Differential Equations
article

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

Michael Ruzhansky, Zahra Keyshams, Zhirayr Avetisyan, Monire Mikaeili Nia
article en

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.

ArXiv.org
Openalex Percentile: Top 50%
Nonlinear Partial Differential Equations
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Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity — Michael Ruzhansky, Zahra Keyshams, et al. · ArXiv.org (2025) | TGRS Research Map | TGRS