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

2021/05/26 by Marianna Chatzakou, Michael Ruzhansky, Chatzakou, M. +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.12862

openalex publication_date 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 of this work which was devoted to the classical Euclidean Klein-Gordon equation.

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• Parabolic Equations with Singular Coefficients and Boundary Data: Analysis and Numerical Simulations
• Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity

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