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June  2013, 3(2): 143-160. doi: 10.3934/mcrf.2013.3.143

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

 1 LMAM, UMR 7122, Université de Lorraine, Ile du Saulcy, 57045 Metz, cedex 1, France 2 UMR-7332, Aix Marseille Université, Centre de Physique Théorique, Campus de Luminy, Case 907, 13288 Marseille, cedex 9, France

Received  February 2012 Revised  May 2012 Published  March 2013

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 is changed to the semi-linear parabolic equation $\partial_tu-\Delta_x u=F(x,t,\sigma(t),u(x,t))$.
Citation: Mourad Choulli, Yavar Kian. Stability of the determination of a time-dependent coefficient in parabolic equations. Mathematical Control & Related Fields, 2013, 3 (2) : 143-160. doi: 10.3934/mcrf.2013.3.143
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