Nonlinear fractional damped wave equation on compact Lie groups

2022/11/11 by Aparajita Dasgupta, Vishvesh Kumar, Dasgupta, Aparajita +3
Engineering · Mathematics · Physics and Astronomy · #35L05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Primary 35L15 #Secondary 35L05 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2211.06155

openalex publication_date 2022/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we deal with the initial value fractional damped wave equation on G, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space for the fractional damped wave equation on G. Moreover, a finite time blow-up result is established under certain conditions on the initial data. In the next part of the paper, we consider fractional wave equation with lower order terms, that is, damping and mass with the same power type nonlinearity on compact Lie groups, and prove the global in-time existence of small data solutions in the energy evolution space.

Related

• Nonlinear fractional wave equation on compact Lie groups
• Semilinear damped wave equation on a compact Lie group with a non-autonomous forcing term
• Fractional semilinear damped wave equation on the Heisenberg group
• Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups
• Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order