arXiv subjects
Publications and source records attributed to Mourad Choulli.
We prove logarithmic stability in the determination of the time-dependent scalar potential in a 1-periodic quantum cylindrical waveguide, from the boundary measurements of the solution to the dynamic Schrödinger equation.
We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $σ(t)$, appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-Δ_x u+σ(t)f(x)u=0$, from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation in changed to the semi-linear parabolic equation $\partial_tu-Δ_x u=F(t,x,σ(t),u(x,t))$.
We prove a stability estimate related to the multi-dimensional Borg-Levinson theorem of determining a potential from spectral data: the Dirichlet eigenvalues and the normal derivatives of the eigenfunctions on the boundary of a bounded domain. The estimate is of Hölder type, and we allow finitely many eigenvalues and normal derivatives to be unknown. We also show that if the spectral data is known asymptotically only, up to $O(k^{-a})$ with $a>>1$, then we still have Hölder stability.