Mostafa Meliani (Radboud University)

Analysis of shape optimization problems in nonlinear acoustics

Wednesday, 26 January 2022, 13:00-14:00 in HG03.085


In various biomedical applications, precise focusing of nonlinear ultrasonic waves is crucial for efficiency and safety of procedures. In this talk, we will discuss the shape sensitivity analysis for a class of optimization problems constrained by general quasi-linear acoustic wave equations that arise in high-intensity focused ultrasound (HIFU) applications, such as the Kuznetsov equation.
To justify the existence and well-definedness of the shape derivative, we will briefly discuss the local well-posedness and regularity of the forward problem, including with respect to shape variations. We will also give an overview of the analysis of the corresponding adjoint problem for a typical cost functional of practical interest and conclude with the expression of a well-defined shape derivative.