Uniqueness and Hölder stability of discontinuous diffusion coefficients in three related inverse problems for the heat equation

Olivier Poisson (1)

1 AMU - Aix Marseille Université

We consider the heat equation ∂ t y − div(c∇y) = H with a discontinuous coefficient in three connected situations. We give uniqueness and stability results for the diffusion coefficient c(·) in the main case from measurements of the solution on an arbitrary part of the boundary and at a fixed time in the whole spatial domain. The diffusion coefficient is assumed to be discontinuous across an unknown interface. The key ingredients are a Carleman–type estimate with non–smooth data near the interface and a stability result for the discontinuous coefficient c(·) in an inverse problem associated with the stationary equation −div(c∇u) = f .

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Poisson. Uniqueness and Hölder stability of discontinuous diffusion coefficients in three related inverse problems for the heat equation. 2007. ⟨hal-01255486⟩