On Carleman estimates with two large parameters

On Carleman estimates with two large parameters

A Carleman estimate for a differential operator P is a weighted energy estimate with a weight of exponential form exp(τφ) that involves a large parameter, τ > 0. The function φ and the operator P need to fulfill some sub-ellipticity properties that can be achieved for instance by choosing φ = exp(αψ), involving a second large parameter, α > 0, with ψ satisfying some geometrical conditions. The ...

Weak Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

Carleman estimates with second large parameter for second order operators

In this paper we prove Carleman type estimates with two large parameters for general linear partial differential operators of second order. By using second large parameter we derive from results for scalar equations first Carleman estimates for dynamical Lamé system with residual stress. We apply these estimates to obtain a Hölder and Lipschitz stability estimates of continuation of solutions o...

Convergent Algorithm Based on Carleman Estimates

Abstract. This article develops the numerical and theoretical study of the reconstruction 5 algorithm of a potential in a wave equation from boundary measurements, using a cost functional built 6 on weighted energy terms coming from a Carleman estimate. More precisely, this inverse problem 7 for the wave equation consists in the determination of an unknown time-independent potential from 8 a si...

Global Carleman estimates for waves and applications

Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality m...