Boundary stabilization of the linear MGT equation with partially absorbing boundary data and degenerate viscoelasticity

Abstract

The Jordan-Moore-Gibson-Thompson (JMGT) equation is a well established and recently widely studied model for nonlinear acoustics (NLA). It is a third-order (in time) semilinear Partial Differential Equation (PDE) model with the distinctive feature of predicting the propagation of ultrasound waves at finite speed due to heat phenomenon know as second sound which leads the hyperbolic character of heat propagation. In this paper we consider the problem of stabilizability of the linear (known as) MGT-equation. We consider a special geometry which is suitable for studying the problem of controlling (from the boundary) the acoustic pressure involved in medical treatments like lithotripsy, thermotherapy, sonochemistry or any other procedures using High Intensity Focused Ultrasound (HIFU).