Stability in the determination of a time-dependent coefficient for wave equations from partial data

作者：Kian Yavar

来源：Journal of Mathematical Analysis and Applications, 2016, 436(1): 408-428.

DOI：10.1016/j.jmaa.2015.12.018

• Inverse problems
• Wave equation
• Scalar time-dependent potential
• Carleman estimates
• Stability inequality

Let Omega be a C-2 bounded domain of R-n, n >= 2, and fix Q = (0,T) x Omega with T > 0. We consider the stability in the inverse problem of determining a time-dependent coefficient of order zero q, appearing in a Dirichlet initial-boundary value problem for a wave equation partial derivative(2)(t)u - Delta(x) u + q(t,x)u = 0 in Q, from partial observations on partial derivative Q. The observation is given by a boundary operator associated to the wave equation. Using suitable geometric optics solutions and Carleman estimates, we prove a stability estimate in the determination of q from the boundary operator.

• 出版日期2016-4-1