The Heat Equation with Singular Potentials. II: Hypoelliptic Case

Abstract

Abstract In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The current work continues and extends the work (Altybay et al. in Appl. Math. Comput. 399:126006, 2021), where the classical heat equation on $\mathbb{R}^{n}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> was considered.