Stability estimate for hyperbolic inverse problem with time dependent coefficient
By Ibtissem Ben Aicha. 2015
48 citations recorded by the source corpus.
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≥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.
Subfields: Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c31ec5d853f29c4410da5e5c329906dd16a6cf37
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term (2016, background): “We also mention the recent works related to the determination of a time-dependent coefficients in IBVP’s for hyperbolic, fractional diffusion and dynamical Schrödinger equations [3, 16, 18, 24, 33, 34, 35].”