An inverse problem for the transmission wave equation with Kelvin–Voigt damping

ABSTRACT

In this paper, we consider a transmission wave problem with Kelvin–Voigt damping in two embedded domains in ${\mathbb{R}}^n$. We construct a global Carleman estimate for the transmission strongly damped wave equation with discontinuous coefficients. With the new Carleman estimate, we prove the Lipschitz stability and uniqueness of the inverse problem of determining the coefficient of the zeroth-order term in the equation with a single measurement observed in any small domain located in the outer domain.

KEYWORDS:

• Wave equation with Kelvin–Voigt damping
• discontinuous coefficients
• global Carleman estimate
• inverse problem
• single measurement

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35R30
• 35L20

Acknowledgments

Finally, we appreciate the reviewer very much for his very good comments for improving this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 51739007 and 11471328]. It is also supported by the Scientific Research of China Hunan Provincial Department of Education [grant number 20C0905].