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Stability in the determination of a time-dependent coefficient for wave equations from partial data (1406.5734v3)

Published 22 Jun 2014 in math.AP

Abstract: We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t2u-\Delta u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $\Omega$ a $C2$ bounded domain of $\mathbb Rn$, $n\geq2$, from partial observations on $\partial Q$. The observation is given by a boundary operator associated to the wave equation. Using suitable complex geometric optics solutions and Carleman estimates, we prove a stability estimate in the determination of $q$ from the boundary operator.

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