Boundary stabilization of nonlinear dynamics of acoustics waves under the JMGT equation
Early Career Math Colloquium
The Jordan–Morse–Gibbson–Thompson (JMGT) equation is a third-order in time partial differential equation (PDE) model describing nonlinear propagation of sound in an acoustic medium. Its study is motivated by a large array of applications arising in engineering and medical sciences, especially high intensity focused ultrasound (HIFU) technologies. The important feature is that the model avoids the infinite speed of propagation paradox associated with the classical second order in time equation known as Westervelt’s equation. The third order in time derivative is due to the shift from parabolic to the hyperbolic model, the latter being a singular perturbation (w.r.t the thermal time relaxation) of the former. In this talk we will present several results pertinent to the model, mostly from the point of view of boundary stabilization. These include: (i) local and global wellposedness, (ii) asymptotic analysis when the thermal relaxation parameter vanishes, and (iii) boundary stabillizability of JMGT in the critical and degenerate case.