Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case

Chatzakou M. Ruzhansky M. Tokmagambetov N.
2022 Taylor and Francis Ltd.

Complex Variables and Elliptic Equations
2022 #67 Issue 3 615 - 632 pp.

In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak solution. Such analysis can be conveniently realised in the setting of graded Lie groups. The uniqueness of the very weak solution, and the consistency with the classical solution are also proved, under suitable considerations. This extends and improves the results obtained in the first part [Altybay et al. Fractional Klein-Gordon equation with singular mass. Chaos Solitons Fractals. 2021;143:Article ID 110579] which was devoted to the classical Euclidean Klein-Gordon equation.

35J05 , 35L03 , 35L05 , 43A70 , Cauchy problem , graded Lie group , Klein–Gordon equation , Rockland operator , very weak solution , weak solution

Text of the article Перейти на текст статьи

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

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

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026