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Preprints, Working Papers, ... Year : 2010

Logarithmic stability in determination of a 3D viscoelastic coefficient and numerical examples

Maya de Buhan
Axel Osses
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Abstract

We proved a Carleman estimate and a sharp unique continuation result for the integro-differential hyperbolic system of the 3D viscoelasticity problem. We used these results to obtain a logarithmic stability estimate for the inverse problem of recovering the spatial part of a viscoelastic coefficient of the form p(x)h(t) from a unique measurement on an arbitrary part of the boundary. The main assumptions are h' (0) = 0, h(0) ≠ 0, p is known in a neighborhood of the boundary and regularity and sensitivity of the reference trajectory. We proposed a method to solve the problem numerically and illustrated the theoretical result by a numerical example.
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Dates and versions

hal-00461159 , version 1 (04-03-2010)

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  • HAL Id : hal-00461159 , version 1

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Maya de Buhan, Axel Osses. Logarithmic stability in determination of a 3D viscoelastic coefficient and numerical examples. 2010. ⟨hal-00461159⟩
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