Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation

Assia Benabdallah (1) , Patricia Gaitan (1) , Jerome Le Rousseau (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We consider the heat equation with a discontinuous diffusion coefficient and give uniqueness and stability results for both the diffusion coefficient and the initial condition from a measurement of the solution on an arbitrary part of the boundary and at some arbitrary positive time. The key ingredient is the derivation of a Carleman-type estimate. The diffusion coefficient is assumed to be discontinuous across interfaces with a monotonicity condition and piecewise constant.

Mots clés: inverse problem; Carleman estimate; non smooth coefficient; parabolic equation

Domaines: Equations aux dérivées partielles [math.AP]

Assia Benabdallah, Patricia Gaitan, Jerome Le Rousseau. Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation. 2006. ⟨hal-00016490v1⟩