The Heat Equation with Singular Potentials. II: Hypoelliptic Case

Chatzakou M. Ruzhansky M. Tokmagambetov N.
June 2022 Springer Science and Business Media B.V.

Acta Applicandae Mathematicae
2022 #179 Issue 1

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 Rⁿ was considered.

Cauchy problem , Graded Lie group , Heat equation , Regularisation , Rockland operator , Singular mass , Very weak solution , Weak solution

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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al–Farabi Kazakh National University, Almaty, Kazakhstan

Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling
Al–Farabi Kazakh National University

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