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

<p style='text-indent:20px;'>The Jordan–Moore–Gibson–Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It third–order (in time) semilinear Partial Differential Equation (PDE) with distinctive feature of predicting the propagation ultrasound waves at <i>finite</i> speed. This due to heat phenomenon known as <i>second sound</i> which leads hyperbolic heat-wave propagation. In this paper, we consider problem in so called "critical" case, where free dynamics unstable. order stabilize, shall use boundary feedback controls supported on portion only. Since remaining part not "controlled", imposed conditions Neumann type fail saitsfy Lopatinski condition, several mathematical issues typical mixed problems within context o stabilizability arise. To resolve these, special geometric constructs along sharp trace estimates will be developed. The are motivated by geometry that suitable modeling controlling (from boundary) acoustic pressure involved medical treatments such lithotripsy, thermotherapy, sonochemistry, or any other procedure involving High Intensity Focused Ultrasound (HIFU).</p>