Recovering density for the Mindlin–Timoshenko system by means of a single boundary measurement

Abstract

In this paper, we consider an inverse problem for the Mindlin–Timoshenko plate system, which is a strongly coupled two-dimensional system consisting of a wave equation and a system of isotropic elasticity, that arises in modeling plate vibrations especially at high frequencies and thicker plates. More precisely, we prove the global uniqueness of recovering the plate density from a single boundary measurement under appropriate geometrical assumptions. Our approach relies on diagonalizing the principal part of the system and making it a system of wave-like equations.

Keywords:

• Inverse problem
• coupled partial differential equation
• Carleman estimate
• Mindlin–Timoshenko system

2010 Mathematics Subject Classifications::

• 35R30
• 35L10

Disclosure statement

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