An inverse problem for Maxwell's equations in a uniaxially anisotropic medium

Impact Factor:1.3

DOI number:10.1016/j.jmaa.2017.06.053

Journal:Journal of Mathematical Analysis and Applications

Key Words:Inverse problem; Maxwell's equations; Uniaxially anisotropic; Carleman estimate

Abstract:We consider Maxwell’s equations for a uniaxially anisotropic and inhomogeneous medium. We discuss an inverse problem of determining the permittivity tensor ⎝ ε_1 0 0 0 ε 0 0 0 ε ⎞ and the permeability tensor ⎛ ⎝ μ_1 0 0 0 μ 0 0 0 μ ⎞ in the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, we prove a stability estimate of Lipschitz type for the inverse problem, provided that ε_1, ε, μ_1, μ satisfy some a priori conditions.

Co-author:Lixia Zhao,Shumin Li,Wuqing Ning

First Author:Yunxia Shang

Indexed by:Journal paper

Document Code:000409565300037

Volume:456

Issue:2

Page Number:1415-1441

Translation or Not:no

Date of Publication:2017-12-15

Links to published journals:https://linkinghub.elsevier.com/retrieve/pii/S0022247X17306145