Stability of the determination of a time-dependent coefficient in parabolic equations

Mourad Choulli; Yavar Kian

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arXiv · 1202.5392

Stability of the determination of a time-dependent coefficient in parabolic equations

Mourad Choulli·Yavar Kian

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Abstract

We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $\sigma(t)$, appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-\Delta_x u+\sigma(t)f(x)u=0$, from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation in changed to the semi-linear parabolic equation $\partial_tu-\Delta_x u=F(t,x,\sigma(t),u(x,t))$.

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Mourad Choulli, Yavar Kian. 2012-02-24. Stability of the determination of a time-dependent coefficient in parabolic equations. https://arxiv.org/abs/1202.5392

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