An inverse problem for Maxwell's equations in isotropic and non-stationary media

Abstract

In this article, we consider Maxwell's equations in an isotropic, inhomogeneous and non-stationary medium. We discuss an inverse problem of determining the t-independent components of the coefficients ϵ, μ in the constitutive relations from a finite number of interior measurements. We prove a Lipschitz stability estimate for the inverse problem by applying the argument on the basis of Carleman estimate.

Keywords:

• inverse problem
• Maxwell's equations
• non-stationary media
• Carleman estimate
• stability

AMS Subject Classifications::

• 35R30
• 35Q61
• 35R25

Acknowledgements

The first author is supported by ‘the Fundamental Research Funds for the Central Universities’. This article was partially finished during the first author's stay at the Graduate School of Mathematical Sciences, The University of Tokyo and during the stay the first author was supported by the twenty-first century COE program at the Graduate School of Mathematical Sciences, The University of Tokyo and the JSPS Postdoctoral Fellowship for Foreign Researchers.