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math.AP2023
Energy decay of some multi-term nonlocal-in-time Moore--Gibson--Thompson equations
Mostafa Meliani, Belkacem Said-Houari
This paper aims to explore the long-term behavior of some nonlocal high-order-in-time wave equations. These equations, which have come to be known as Moore--Gibson--Thompson equati…
math.AP2023
The Kuznetsov and Blackstock equations of nonlinear acoustics with nonlocal-in-time dissipation
B. Kaltenbacher, M. Meliani, V. Nikolić
In ultrasonics, nonlocal quasilinear wave equations arise when taking into account a class of heat flux laws of Gurtin--Pipkin type within the system of governing equations of soun…
math.AP2023
A unified analysis framework for generalized fractional Moore--Gibson--Thompson equations: Well-posedness and singular limits
Mostafa Meliani
In acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In this work, we analyze i…