arXiv subjects
Publications and source records attributed to Laure Cardoulis.
In this paper, we consider the Dirichlet Laplacian operator -Δ on a curved quantum guide in R n (n = 2, 3) with an asymptotically straight reference curve. We give uniqueness results for the inverse problem associated to the reconstruction of the curvature by using either observations of spectral data or a boot-strapping method. keywords: Inverse Problem, Quantum Guide, Curvature
This article is devoted to prove a stability result for two independent coefficients for a Schrödinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain.
We consider the operator $H:= i \partial_t + \nabla \cdot (c \nabla)$ in an unbounded strip $Ω$ in $\mathbb{R}^2$, where $c(x,y) \in \mathcal{C}^3(\barΩ)$. We prove adapted a global Carleman estimate and an energy estimate for this operator. Using these estimates, we give a stability result for the diffusion coefficient $c(x,y)$.