A Carleman estimate for the linear magnetoelastic waves system and an inverse source problem in a bounded conductive medium

ABSTRACT

In this paper, we consider an inverse problem for the simultaneous diffusion process of elastic and electromagnetic waves in an isotropic heterogeneous elastic body which is identified with an open bounded domain. From the mathematical point of view, the system under consideration can be viewed as the coupling between the hyperbolic system of elastic waves and a parabolic system for the magnetic field. We study an inverse problem of determining the external source terms by observations data in a neighborhood of the boundary and we prove the Hölder stability. For the proof, we show a Carleman estimate for the displacement and the magnetic field of the magnetoelastic system.

KEYWORDS:

• Magnetoelastic waves
• Carleman estimates
• inverse problems
• stability

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 35Q35
• 35R30

Acknowledgements

The authors would like to thank the referees for their valuable comments which helped to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research of M. Yamamoto is supported by Grant-in-Aid for Scientific Research (S) 15H05740 and A3 Foresight Program Modeling and Computation of Applied Inverse Problems of Japan Society for the Promotion of Science, and by the “RUDN University Program 5-100”, NSFC [grant numbers 11771270, 91730303].