标题： 热方程的非常弱解，具有各向异性奇时变扩散率 显示英文标题

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

摘要： 我们研究带有时间依赖性、各向异性且可能奇异的扩散张量的热方程。 由于在此设置下弱（在Sobolev意义下）或分布解可能不存在，我们采用非常弱解的框架来建立具有奇异、各向异性、时间依赖性扩散张量的热方程解的存在性和唯一性。 显示英文摘要

摘要： 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.