Stability estimate in the determination of a time-dependent coefficient for hyperbolic equation by partial Dirichlet-to-Neumann map

ABSTRACT

In this paper, we obtain stability estimates of recovery a time dependent coefficient $q(t,x)$ in a wave equation, from partial observations on $\mathrm{\partial }Q$. We show in dimension n greater than two a log-type stability estimate in the determination of q from the local Dirichlet-to-Neumann map. Additionally, we prove that it can be stably recovered in a larger region of the domain by enlarging the set of data.

KEYWORDS:

• Inverse problem
• wave equation
• Carleman estimates
• time dependent coefficient
• stability estimate
• light ray transform

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 35L05
• 35L20
• Secondary:34A55

Disclosure statement

No potential conflict of interest was reported by the authors.