Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Control and Optimization Year : 2007

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

Abstract

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.
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Dates and versions

hal-00016490 , version 1 (05-01-2006)
hal-00016490 , version 2 (18-05-2006)
hal-00016490 , version 3 (20-10-2006)

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Cite

Assia Benabdallah, Patricia Gaitan, Jérôme Le Rousseau. Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation. SIAM Journal on Control and Optimization, 2007, 46 (5), pp.1849-1881. ⟨10.1137/050640047⟩. ⟨hal-00016490v3⟩
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