1 citations · 1 across the 7 of their papers we have counts for
7 papers
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…
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…
Limiting behavior of quasilinear wave equations with fractional-type dissipation
Barbara Kaltenbacher, Mostafa Meliani, Vanja Nikolić
In this work, we investigate a class of quasilinear wave equations of Westervelt type with, in general, nonlocal-in-time dissipation. They arise as models of nonlinear sound propag…
Analysis of general shape optimization problems in nonlinear acoustics
Mostafa Meliani, Vanja Nikolić
In various biomedical applications, precise focusing of nonlinear ultrasonic waves is crucial for efficiency and safety of the involved procedures. This work analyzes a class of sh…