4 papers · 1 filter
Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation
Mostafa Meliani, Belkacem Said-Houari
In nonlinear 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 the literatur…
Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation
Mostafa Meliani, Belkacem Said-Houari
In this paper, we consider the Jordan--Moore--Gibson--Thompson with a time-fractional damping term of the type $δ\textup{D}_t^{1-α} Δ\psit$ where we allow the challenging so-called…
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…
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…