Journal
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Volume 67, Issue 3, Pages 615-632Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17476933.2021.1950146
Keywords
Klein-Gordon equation; Rockland operator; Cauchy problem; graded Lie group; weak solution; very weak solution
Categories
Funding
- Fonds Wetenschappelijk Onderzoek (FWO) [G.0H94.18N]
- Methusalem programme of the Ghent University Special Research Fund (BOF) [01M01021]
- Engineering and Physical Sciences Research Council (EPSRC) [EP/R003025/2]
- EPSRC [EP/R003025/2] Funding Source: UKRI
Ask authors/readers for more resources
In this paper, a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spatial variable is considered, and a very weak solution is proved. The analysis is conveniently realized in the setting of graded Lie groups. The uniqueness of the very weak solution and its consistency with the classical solution are also demonstrated, extending and improving previous results on the classical Euclidean Klein-Gordon equation.
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available