  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
\textit{finite} speed due to heat phenomenon know as \textit{second sound}
which leads to 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 that 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).
