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The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established andrecently widely studied model for nonlinear acoustics (NLA). It is athird-order (in time) semilinear Partial Differential Equation (PDE) model withthe 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, weconsider the problem of stabilizability of the linear (known as) MGT--equation.We consider a special geometry that is suitable for studying the problem ofcontrolling (from the boundary) the acoustic pressure involved in medicaltreatments like lithotripsy, thermotherapy, sonochemistry, or any otherprocedures using High Intensity Focused Ultrasound (HIFU).

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