Recovery of time-dependent damping coefficients and potentials appearing in wave equations from partial data

2016/03/31 by Kian, Yavar
#35L05 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.09600

Abstract

We consider the inverse problem of determining a time-dependent damping coefficient a and a time-dependent potential q, appearing in the wave equation ∂_t²u-Δ_x u+a(t,x)∂_tu+q(t,x)u=0 in Q=(0,T)×Ω, with T>0 and Ω a \mathcal C² bounded domain of \mathbb Rⁿ, n≥2, from partial observations of the solutions on ∂ Q. More precisely, we look for observations on ∂ Q that allow to determine uniquely a large class of time-dependent damping coefficients a and time-dependent potentials q without involving an important set of data. We prove global unique determination of a∈ W^1,p(Q), with p>n+1, and q∈ L^∞(Q) from partial observations on ∂ Q.

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