Stable determination outside a cloaking region of two time-dependent coefficients in an hyperbolic equation from Dirichlet to Neumann map

2016/05/11 by Mourad Bellassoued, Bellassoued, Mourad, Aicha, Ibtissem Ben
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Microwave Imaging and Scattering Analysis

paper · pdf · doi:10.48550/arxiv.1605.03466

Abstract

In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension n≥ 2, stability estimates with respect to the Dirichlet-to-Neumann map of these coefficients provided that are known outside a cloaking regions. Moreover, we prove that it can be stably recovered in larger subsets of the domain by enlarging the set of data

Citations

• Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

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