2021/07/21 by Marcelo Bongarti, Irena Lasiecka, Bongarti, Marcelo +3
Computer Science · Engineering · Mathematics · #35LXX #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2107.09978
openalex publication_date 2021/07/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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 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).