Unique determination of a time-dependent potential for wave equations from partial data

Yavar Kian

Published 2015-05-24Version 1

We consider the inverse problem of determining a time-dependent coefficient of order zero $q$, appearing in a wave equation $\partial_t^2u-\Delta u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $\Omega$ a $C^2$ bounded domain of $\mathbb R^n$, $n\geq2$, from partial observations of the solutions on $\partial Q$. Using suitable geometric optics solutions and Carleman estimates, we prove global unique determination of a coefficient $q\in L^\infty(Q)$ from these observations.