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arXiv · 1711.09276

Carleman estimate for linear viscoelasticity equations and an inverse source problem

Oleg Imanuvilov·Masahiro Yamamoto
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Abstract

We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove a Carleman estimate with boundary values of solutions of viscoelasticity system. Since a solution $u$ under consideration is not assumed to have compact support, in the decoupling of the Lam\'e operator by introducing div $u$ and rot $u$, we have no boundary condition for them, so that we have to carry out arguments by a pseudodifferential operator. Second we apply the Carleman estimate to an inverse source problem of determining a spatially varying factor of the external source in the linear viscoelastitiy by extra Neumann data on the lateral subboundary over a sufficiently long time interval and establish the stability estimate.

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Oleg Imanuvilov, Masahiro Yamamoto. 2017-11-25. Carleman estimate for linear viscoelasticity equations and an inverse source problem. https://arxiv.org/abs/1711.09276

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