arXiv subjects
Publications and source records attributed to Abbes Benaissa.
A degenerate Schrödinger equation under fractional integral damping is considered. Here the damping term is singular and not integrable and we consider the two cases when damping acting on the degenerate boundary and nondegenerate boundary. In this paper, we establish polynomial energy decay rates for the degenerate Schrödinger equation by using resolvent estimates.
In this paper we study the well-posedness and stability of degenerate Schrödinger equation with a fractional boundary damping. First, we establish the well-posedness of the degenerate problem $ψ_t(x,t)-\imath(τ(x) ψ_x(x,t))_x=0, \hbox{ with } x \in (0,1)$, controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decay rate of the solution are established using multiplier method.
This paper is devoted to study the well-posedness and stability of degenerate Schrödinger equation with a boundary control acting at the degeneracy. First, we establish the well-posedness of the degenerate problem $v_t(x,t)+\imath(x^αv_x(x,t))_x=0, \hbox{ with } x \in (0,1)$, controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decreasing of the solution are established. This result is optimal and it is obtained using complex analysis method.
We study polynomial stability to the one-dimensional system in the linear isothermal theory of swelling porous elastic soils with an internal fractional damping. We establish an optimal decay result by frequency domain method
In this paper, we consider the well-posedness and stability of a one-dimensional system of degenerate wave equations coupled via zero order terms with one boundary fractional damping acting on one end only. We prove optimal polynomial energy decay rate of order $1/t^{(3-τ)}$. The method is based on the frequency domain approach combined with multiplier technique.