Preprint 2025-05
Fahim Aslam, Zayd Hajjej, Jianghao Hao, Mauricio Sepúlveda:
Global existence and asymptotic profile of an infinite memory logarithmic wave equation with fractional derivative and strong damping
Abstract:
This paper investigates the global existence and long-term behavior of solutions to a logarithmic wave equation incorporating infinite memory, fractional derivative, and strong damping in a bounded domain. The equation features a nonlinear logarithmic source term, which is significant in various physical applications such as structural vibrations, fluid dynamics, and quantum mechanics. The presence of strong damping and fractional derivative terms is crucial in ensuring well-posedness and stabilizing the system, while the infinite memory term introduces a complex history-dependent dynamic. This manuscript is a continuation of recent work by the first two authors (Nonlinear logarithmic wave equations: Blow-up phenomena and the influence of fractional damping, infinite memory, and strong dissipation, Evol. Equ. Control Theory, 13(2024), 1423--1435). In addition, numerical simulations are presented to illustrate the asymptotic behavior of solutions.
