arXiv subjects

Moez Khenissi

Publications and source records attributed to Moez Khenissi.

11 recordsLinked to original sources

arXiv2024

Stability analysis of inverse problems for coupled magnetic Schrödinger equations

We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schrödinger equation in a bounded domain of $\mathbb{R}^d$, $d \ge 2$, from finitely many partial boundary measurements of the solution. We prove that these $3d+3$ unknown scalar coefficients can be Hölder stably retrieved by $(3d+2)$-times suitably changing the initial condition attached at the system.

math.AP↗

arXiv2024

Indirect stabilization of semilinear coupled wave systems

In this paper, we study the indirect stabilization problem for a system of two coupled semilinear wave equations with internal damping in a bounded domain in $\mathbb{R}^3$. The nonlinearity is assumed to be subcritical, defocusing and analytic. Under geometric control condition on both coupling and damping regions, we establish the exponential energy decay rate.

math.AP↗

arXiv2020

Blow-up of semi-discrete solution of a nonlinear parabolic equation with gradient term

This paper is concerned with approximation of blow-up phenomena in nonlinear parabolic problems. We consider the equation u_t = u_xx +|u|^p -b(x)|u_x|^q in a bounded domain, we study the behavior of the semidiscrete problem. Under some assumptions we show existence and unicity of the semidiscrete solution, we show that it blows up in a finite time and we prove the convergence of the semidiscrete problem. Finally, we give an approximation of the blow up rate and the blow up time of the semidiscrete solution

math.AP↗

arXiv2016

On the stability of the Bresse system with frictional damping

In this paper, we consider the Bresse system with frictional damping terms and prove some optimal decay results for the $L^2$-norm of the solution and its higher order derivatives. In fact, if we consider just one damping term acting on the second equation of the solution, we show that the solution does not decay at all. On the other hand, by considering one damping term alone acting on the third equation, we show that this damping term is strong enough to stabilize the whole system. In this case, we found a completely new stability number that depends on the parameters in the system. In addition, we prove the optimality of the results by using eigenvalues expansions. Our obtained results have been proved under some assumptions on the wave speeds of the three equations in the Bresse system.

math.AP↗

arXiv2015

On a Finite Differnce Scheme For Blow Up Solutions For The Chipot-Weissler Equation

In this paper, we are interested in the numerical analysis of blow up for the Chipot-Weissler equation with Dirichlet boundary conditions in bounded domain. To approximate the blow up solution, we construct a finite difference scheme and we prove that the numerical solution satisfies the same properties of the exact one and blows up in finite time.

math.NA↗

arXiv2015

Local energy decay and smoothing effect for the damped Schr{ö}dinger equation

We prove the local energy decay and the smoothing effect for the damped Schr{ö}dinger equation on R^d. The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation which we consider.

math-ph↗

arXiv2015

Energy decay for linear dissipative wave equations in exterior domains

In earlier works, we have shown the uniform decay of the local energy of the damped wave equation in exterior domain when the damper is spatially localized near captive rays. In order to have uniform decay of the total energy, the damper has also to act at space infinity. In this work, we establish uniform decay of both the local and global energies. The rates of decay turns out to be the same as those for the heat equation, which shows that an effective damper at space infinity strengthens the parabolic structure in the equation.

math.AP↗

arXiv2015

Asymptotic Behaviours of Solutions for Finite Difference Analogue of the Chipot-Weissler Equation

This paper deals with nonlinear parabolic equation for which a local solution in time exists and then blows up in a finite time. We consider the Chipot-Weissler equation. We study the numerical approximation, we show that the numerical solution converges to the continuous one under some restriction on the initial data and the parameters of the non linearity. Moreover, we study the numerical blow up sets and we show that although the convergence of the numerical solution is guaranteed, the numerical blow up sets are sometimes different from that of the PDE

math.NA↗

arXiv2012

The Kato Smoothing Effect for Regularized Schrödinger Equations in Exterior Domains

We prove, under the exterior geometric control condition, the Kato smoothing effect for solutions of an inhomogenous and damped Schrödinger equation on exterior domains.

math.AP↗

arXiv2012

Smoothing effect for the regularized Schrödinger equation with non controlled orbits

We prove that the geometric control condition is not necessary to obtain the smoothing effect and the uniform stabilization for the strongly dissipative Schrödinger equation.

math.AP↗

arXiv2007

On the stabilization of the elasticity system by the boundary

We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary.

math.AP↗