Nonlinear fractional damped wave equation on compact Lie groups

Article type: Research Article

Authors: Dasgupta, Aparajita^a | Kumar, Vishvesh^b | Mondal, Shyam Swarup^{a; *}

Affiliations: [a] Department of Mathematics, Indian Institute of Technology Delhi, Delhi, 110016, India | [b] Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, B 9000 Ghent, Belgium

Correspondence: [*] Corresponding author. E-mail: mondalshyam055@gmail.com.

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, i.e., 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.

Keywords: Fractional damped wave equation, well-posedness, compact Lie groups, L²–L²-estimates, finite blow-up

DOI: 10.3233/ASY-231842

Journal: Asymptotic Analysis, vol. 134, no. 3-4, pp. 485-511, 2023