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We consider a 2×2 system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse problems of determining some or all of the coefficients by observations in an arbitrary subdomain over a time interval of only one… (More)

- Assia Benabdallah, Patricia Gaitan, Jérôme Le Rousseau
- SIAM J. Control and Optimization
- 2007

We consider the operator H := i∂t + ∇ · (c∇) in an unbounded strip Ω in R 2 , where c(x, y) ∈ C 3 (Ω). 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).

- Michel Cristofol, Patricia Gaitan, Hichem Ramoul
- 2006

For a two by two reaction-diffusion system on a bounded domain we give a simultaneous stability result for one coefficient and for the initial conditions. The key ingredient is a global Carleman-type estimate with a single observation acting on a subdomain.

A new Carleman inequality for parabolic systems with a single observation and applications Une nouvelle inégalité de Carleman pour des systèmes paraboliques avec une seule observation et applications a r t i c l e i n f o a b s t r a c t In this Note, we present Carleman estimates for linear reaction–diffusion–convection systems of two equations and linear… (More)

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.

- Patricia Gaitan, Hiroshi Isozaki, Olivier Poisson, Samuli Siltanen, Janne P. Tamminen
- SIAM J. Math. Analysis
- 2013

An inverse boundary value problem for the heat equation is considered on the interval (0, 1), where the heat conductivity γ(t, x) is piecewise constant and the point of discontinuity depends on time: γ(t, x) = k 2 for 0 < x < s(t) and γ(t, x) = 1 for s(t) < x < 1. It is shown that k and s(t) on the time interval [0, T ] are determined from the partial… (More)

We study the inverse problem of the simultaneous identification of two discontinuous diffusion coefficients for a one-dimensional coupled parabolic system with the observation of only one component. The stability result for the diffusion coefficients is obtained by a Carleman-type estimate. Results from numerical experiments in the one-dimensional case are… (More)

- Patricia Gaitan
- 2008

For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincaré-type estimate and an energy estimate with a single observation acting on a part of the boundary.

We consider a 2×2 system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse problems of determining some or all of the coefficients by observations in an arbitrary subdomain over a time interval of only one… (More)

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