Geodesic
Unique determination of a time-dependent potential for wave equations from partial data
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 4, pp. 973-990

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We consider the inverse problem of determining a time-dependent potential q, appearing in the wave equation ∂t2u−Δxu+q(t,x)u=0 in Q=(0,T)×Ω with T>0 and Ω a C2 bounded domain of Rn, n⩾2, from partial observations of the solutions on ∂Q. More precisely, we look for observations on ∂Q that allows to recover uniquely a general time-dependent potential q without involving an important set of data. We prove global unique determination of q∈L∞(Q) from partial observations on ∂Q. 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.

DOI : 10.1016/j.anihpc.2016.07.003
Classification : 35R30, 35L05
Keywords: Inverse problems, Wave equation, Time-dependent potential, Uniqueness, Carleman estimates, Partial data 
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     author = {Kian, Yavar},
     title = {Unique determination of a time-dependent potential for wave equations from partial data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {973--990},
     publisher = {Elsevier},
     volume = {34},
     number = {4},
     year = {2017},
     doi = {10.1016/j.anihpc.2016.07.003},
     mrnumber = {3661867},
     zbl = {1435.35416},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2016.07.003/}
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Kian, Yavar. Unique determination of a time-dependent potential for wave equations from partial data. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 4, pp. 973-990. doi: 10.1016/j.anihpc.2016.07.003

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