Laure Cardoulis

Inverse Problem for a Curved Quantum Guide

In this paper, we consider the Dirichlet Laplacian operator −∆ 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

Inverse Problem for the Schrödinger Operator in an Unbounded Strip

Abstract We consider the operator H := i∂t + ∇ . (c∇) in an unbounded strip Ω in ℝ2, where . We prove an adapted 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).

Inverse problem for the Schrodinger operator in an unbounded strip

We consider the operator H:= iδt + ∇ (c∇) in an unbounded strip ω in 2, where c(x, y) C3(ω). We prove an adapted 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).

An inverse spectral problem for a Schrödinger operator with an unbounded potential

In this paper, we prove a uniqueness theorem for the potential

An inverse problem for the heat equation in an unbounded guide

V(x)

Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.

of the following Schrodinger operator

Identification of two independent coefficients with one observation for the Schrödinger operator in an unbounded strip

H=-\Delta +q(\vert x \vert)+V(x) \mbox{ in } \mathbb{R}^2

Inverse problem for the Schrödinger operator in an unbounded strip

, where

An inverse problem for a time-dependent Schrödinger operator in an unbounded strip

q(\vert x \vert)

Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr

is a known increasing radial potential satisfying