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arxiv: 1505.06498 · v3 · pith:Q34MSA46new · submitted 2015-05-24 · 🧮 math.AP

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

classification 🧮 math.AP
keywords partialdeterminationobservationsomegapotentialtime-dependentuniquewave
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We consider the inverse problem of determining a time-dependent potential $q$, appearing in the 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 $\partial Q$. We prove global unique determination of a coefficient $q\in L^\infty(Q)$ from these observations.

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