Interactions of nonlinear acoustic waves with different physical phenomena, such as heat transfer or oscillations of microbubbles, are central to many innovative ultrasound applications ranging from non-invasive cancer treatments to contrast-enhanced imaging and targeted drug delivery. Model-based optimization methods offer powerful tools for controlling these procedures, but the complexity of the underlying multiphysics systems, which in soft biological media also involve time-fractional attenuation, has largely prevented their efficient use.
This project will develop new mathematical methodologies for a class of nonlinear differential equations modeling such interactions. We will address open questions about the properties of the underlying systems and leverage these insights to design more efficient numerical methods for their simulation and control.
