87 citations · 268 across the 23 of their papers we have counts for
26 papers · 1 filter
Global well-posedness and Decay estimates for solutions of the Navier--Stokes--Maxwell system
Belkacem Said-Houari
We investigate the global solvability and the large-time asymptotic behavior of solutions to the Navier--Stokes--Maxwell system in two and three space dimensions. The system descri…
Optimal Time-Decay of global solutions to the Navier-Stokes-Maxwell system
Haroune Houamed, Slim Ibrahim, Belkacem Said-Houari
We prove the existence and uniqueness of global-in-time solutions to the Navier--Stokes--Maxwell (NSM) system for small initial data in the critical Fujita--Kato space $\dot H^{\fr…
On the decay estimates of a nonlocal convection-diffusion Hamer system
Timothée Crin-Barat, Belkacem Said-Houari
We consider the multi-dimensional Hamer model for radiating gases in its coupled hyperbolic--elliptic formulation. By means of energy estimates, we establish the global well-posedn…
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…
Global existence and asymptotic behavior of the Westervelt--hyperbolic Pennes system
Imen Benabbas, Belkacem Said-Houari
In this work, we investigate the global existence and asymptotic behavior of a mathematical model of nonlinear ultrasonic heating based on a coupled system of the Westervelt equati…
Global unique solutions to the planar inhomogeneous Navier--Stokes--Maxwell equations
Diogo Arsénio, Haroune Houamed, Belkacem Said--Houari
The evolution of an electrically conducting imcompressible fluid with nonconstant density can be described by a set of equations combining the continuity, momentum and Maxwell's eq…
Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating
Imen Benabbas, Belkacem Said-Houari
In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parame…
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 Westervelt--Pennes--Cattaneo model: local well-posedness and singular limit for vanishing relaxation time
Imen Benabbas, Belkacem Said-Houari
In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on a coupled system of the Westervelt equation and the hyperbolic Pennes bioheat equation (W…
Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics
Vanja Nikolić, Belkacem Said-Houari
High frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock's acoustic wave equation with strong d…
Local well-posedness of a coupled Westervelt-Pennes model of nonlinear ultrasonic heating
Vanja Nikolić, Belkacem Said-Houari
High-Intensity Focused Ultrasound (HIFU) waves are known to induce localized heat to a targeted area during medical treatments. In turn, the rise in temperature influences their sp…
Global existence for the Jordan--Moore--Gibson--Thompson equation in Besov spaces
Belkacem Said-Houari
In this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named the Jordan--Moore--Gibson--Thompson equation. This equation arises as an alternative model to…
Global well-posedness of the Cauchy problem for the Jordan--Moore--Gibson--Thompson equation with arbitrarily large higher-order Sobolev norms
Belkacem Said-Houari
In this paper, we consider the 3D Jordan--Moore--Gibson--Thompson equation arising in nonlinear acoustics. First, we prove that the solution exists globally in time provided that t…
Asymptotic behavior of nonlinear sound waves in inviscid media with thermal and molecular relaxation
Vanja Nikolić, Belkacem Said-Houari
Ultrasonic propagation through media with thermal and molecular relaxation can be modeled by third-order in time nonlinear wave-like equations with memory. This paper investigates…
Stability of Couette flow for 2D Boussinesq system without thermal diffusivity
Nader Masmoudi, Belkacem Said-Houari, Weiren Zhao
In this paper, we prove the stability of Couette flow for 2D Navier-Stokes Boussinesq system without thermal diffusivity for the initial perturbation in Gevrey-, ($1/3…
On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity
Vanja Nikolić, Belkacem Said-Houari
We prove global solvability of the third-order in time Jordan-More-Gibson-Thompson acoustic wave equation with memory in , where . This wave equation models…
Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains
Vanja Nikolić, Belkacem Said-Houari
Motivated by the propagation of nonlinear sound waves through relaxing hereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson acoustic wave equation. Under…
On the Cauchy problem for the standard linear solid model with heat conduction: Fourier versus Cattaneo
Marta Pellicer, Belkacem Said-Houari
In this paper, we consider the standard linear solid model in coupled, first, with the Fourier law of heat conduction and, second, with the Cattaneo law. First, we g…
Nonlinear Damped Timoshenko Systems with Second Sound - Global Existence and Exponential Stability
Salim A. Messaoudi, Michael Pokojovy, Belkacem Said-Houari
In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one-dimensional bounded domain. The system has two dissipative mechanisms being present in the eq…
On the stability of the Bresse system with frictional damping
Tej-Eddine Ghoul, Moez Khenissi, Belkacem Said-Houari
In this paper, we consider the Bresse system with frictional damping terms and prove some optimal decay results for the -norm of the solution and its higher order derivatives.…
Wellposedness and decay rates for the Cauchy problem of the Moore-Gibson-Thompson equation arising in high intensity ultrasound
Marta Pellicer, Belkacem Said-Houari
In this paper, we study the Moore--Gibson--Thompson equation in , which is a third order in time equation that arises in viscous thermally relaxing fluids and also in…
Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions
Stéphane Gerbi, Belkacem Said-Houari
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the…
Existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term
Stéphane Gerbi, Said-Houari Belkacem
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the wei…