Stability estimate for hyperbolic inverse problem with time dependent coefficient

Abstract

We study the stability in the inverse problem of determining the time dependent zeroth-order coefficient $q(t,x)$ arising in the wave equation, from boundary observations. We derive, in dimension $n\ge 2$, a log-type stability estimate in the determination of $q$ from the Dirichlet-to-Neumann map, in a subset of our domain assuming that it is known outside this subset. Moreover, we prove that we can extend this result to the determination of $q$ in a larger region, and then in the whole domain provided that we have much more data.

Cited by in corpus (10)

• The Inverse Problem for the Dirichlet-to-Neumann map on Lorentzian manifolds
• The Light Ray transform in Stationary and Static Lorentzian geometries
• Stability estimate for an inverse problem for the Schr{ö}dinger equation in a magnetic field with time-dependent coefficient
• The Light Ray transform on Lorentzian manifolds
• Recovery of non-smooth coefficients appearing in anisotropic wave equations
• Determining the time dependent matrix potential in a wave equation from partial boundary data
• Stability estimates for relativistic Schrödinger equation from partial boundary data
• A uniqueness result for light ray transform on symmetric 2-tensor fields
• Stability estimate for a partial data inverse problem for the convection-diffusion equation
• Uniqueness Result For Semi-linear Wave Equations With Sources