Belhassen Dehman

Belhassen Dehman
University of Tunis El Manar | FST · Department of Mathematics

Professor

About

23
Publications
1,193
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418
Citations
Citations since 2016
1 Research Item
240 Citations
2016201720182019202020212022010203040
2016201720182019202020212022010203040
2016201720182019202020212022010203040
2016201720182019202020212022010203040

Publications

Publications (23)
Article
Full-text available
The goal of this note is to prove observability estimates for the wave equation with a density which is only continuous in the domain, and satisfies some multiplier-type condition only in the sense of distributions. Our main argument is that one can construct suitable approximations of such density by a sequence of smooth densities whose correspond...
Article
Full-text available
In this article, we prove an exact boundary controllability result for the isotropic elastic wave system in a bounded domain Ω of ℝ3. This result is obtained under a microlocal condition linking the bicharacteristic paths of the system and the region of the boundary on which the control acts. This condition is to be compared with the so-called Geom...
Article
In this article, we consider the wave equation in a bounded domain Ω of ℝd with a potential q . Our goal then is to show that the high-frequency part of the corresponding solutions weakly depends on the potential. We will in particular focus on two instances of interest arising in data assimilation and control theory, respectively corresponding to...
Article
We consider the exact controllability problem on a compact manifold Ω for two coupled wave equations, with a control function acting on one of them only. Action on the second wave equation is obtained through a coupling term. First, when the two waves propagate with the same speed, we introduce the time {T_{ω → {O} → ω}} for which all geodesics tra...
Chapter
The aim of this article is to prove a stabilization theorem for the semilinear wave equation on a bounded open domain of ℝd , d ⩾ 1 with boundary Dirichlet condition. More precisely, we study systems of the type $$ \left\{ \begin{gathered} \square u + a\left( x \right)\partial _t u + f\left( u \right) = 0 on\left] {0, + \infty } \right[x\Omega \hfi...
Article
Full-text available
In three dimension space, under a microlocal geometric condition, we give the rate of decay of the local energy for solutions of the Lamé system on exterior domain, with localized nonlinear damping.
Article
Null-controllability for the wave equation is studied in the context of dis- tributed linear constraints on the control.
Article
We present a regularity result for the HUM optimal control associated with the interior control of linear waves. We use this analysis, together with Strichartz inequalities, to get results on the exact controllability for subcritical nonlinear waves in a bounded domain of ℝ3.
Article
In this paper, we study the stabilization property and the exact controllability for the nonlinear Schrödinger equation on a two dimensional compact Riemannian manifold, without boundary. We use a pseudo-differential dissipation. The proofs are based on a result of propagation of singularities and on recent dispersion estimates (Strichartz type ine...
Article
In this paper, we analyze the exponential decay property of solutions of the semilinear wave equation in R3 with a damping term which is effective on the exterior of a ball. Under suitable and natural assumptions on the nonlinearity we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is...
Article
Dans ce travail, nous construisons des solutions pour une certaine classe d'équations semi-linéaires complexes dans le plan. Plus précisément on considère prés d'un point XQ de R ² l'équation où P est un opérateur différentiel d'ordre m(m ≧ 1) à coefficients C ∞ complexes, et o ù ƒest à valeurs complexes, analytique en et seulement C ∞ en x. En sup...
Article
We prove local existence in dimension 2, of regular solutions for a class of quasi-linear differential operators of order 1 and complex coefficients. More precisely, we deal with equations of type D t u+c(t,x,u)D x u=g(t,x,u), where c and g are C ∞ of their arguments, analytic in u and with complex values. This result is shown under a “sign” hypoth...

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