Relating models of nonlinear acoustics through singular limit analysis
Accurate mathematical modeling of nonlinear sound propagation is relevant in various applications of ultrasonic waves, ranging from imaging to lithotripsy and cancer therapy. In this talk, we will discuss how different (non)local PDE models arising in nonlinear acoustics can be related in the limit of relevant small parameters, such as sound diffusivity and thermal relaxation time. In particular, we will quantify the errors made when replacing (singularly) perturbed acoustic models with unperturbed ones. The talk is based on joint works with Barbara Kaltenbacher (University of Klagenfurt) and Mostafa Meliani (Radboud University).
