Dynamic of Logarithmically and Fractionally Damped Wave Equations With Strong Damping and Infinite Memory: Theory and Numerics
This paper addresses the global existence and asymptotic behavior of solutions to a logarithmic wave equation posed in a bounded domain and incorporating strong damping, a fractional time derivative, and an infinite-memory term. The model includes a nonlinear logarithmic source, which arises in various physical contexts such as structural vibrations, fluid dynamics, and quantum mechanics. The combined effects of strong damping and fractional dissipation are essential for ensuring well-posedness and system
stabilization, while the infinite-memory term introduces a complex, history-dependent dynamic. This study extends the recent work of 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) by establishing new results on global dynamics. Numerical simulations are also provided to illustrate the long-term behavior of solutions and support the theoretical
findings.
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This paper addresses the global existence and asymptotic behavior of solutions to a logarithmic wave equation posed in a bounded domain and incorporating strong damping, a fractional time…