Unique determination of a time-dependent potential for wave equations from partial data
Yavar Kian
Aix Marseille Univ., Université de Toulon, CNRS, CPT, Marseille, France
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Abstract
We consider the inverse problem of determining a time-dependent potential , appearing in the wave equation in with and a bounded domain of , , from partial observations of the solutions on . More precisely, we look for observations on that allows to recover uniquely a general time-dependent potential without involving an important set of data. We prove global unique determination of from partial observations on . Besides being nonlinear, this problem is related to the inverse problem of determining a semilinear term appearing in a nonlinear hyperbolic equation from boundary measurements.
Cite this article
Yavar Kian, Unique determination of a time-dependent potential for wave equations from partial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 4, pp. 973–990
DOI 10.1016/J.ANIHPC.2016.07.003