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Article Dans Une Revue Mathematical Control and Related Fields Année : 2013

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

Résumé

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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Dates et versions

hal-00673690 , version 1 (24-02-2012)
hal-00673690 , version 2 (28-02-2012)

Identifiants

Citer

Mourad Choulli, Yavar Kian. Stability of the determination of a time-dependent coefficient in parabolic equations. Mathematical Control and Related Fields, 2013, 3 (2), pp.143-160. ⟨10.3934/mcrf.2013.3.143⟩. ⟨hal-00673690v2⟩
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