Colloquium: Sebastian Acosta (Baylor College of Medicine)

About this event

Title: Mathematics of nonlinear ultrasound imaging: Advances and open problems. Abstract: The Westervelt equation models the propagation of high-intensity ultrasound waves. For medical imaging purposes, it is needed to estimate the parameters in the equation that model wave speed, diffusivity, and nonlinearity. I will discuss up to date progress on this problem, as well as open questions, from the mathematical point of view. I will also present our contribution which shows that by using time-periodic solutions excited from the boundary at a sufficiently high frequency, knowledge of the first- and second-harmonic Cauchy data at the boundary is sufficient to simultaneously determine the wave speed, diffusivity and nonlinearity in the interior of the domain of interest.