Free boundary problems in biology and fluid dynamics

The research group Análisis Matemático Aplicado y Ecuaciones Diferenciales (AMAED) are organizing the event "Free boundary problems in biology and fluid dynamics" at Universidad de Cantabria. This event will take place on the September 12th, 13th and 14th in Santander (Spain).

Partial differential equations (PDEs) describe most of the physical and chemical phenomena in nature. In that regards, it is not surprinsing that PDEs are also becoming increasingly popular among biologist in order to accurately portray different events. In many of these applications to physics, chemistry and also biology, fluid-solid interactions play a crucial role. As an example, one may consider the motion of spermatozoa within the fluid. There, the different spermatozoa, when swimming, interact with the fluid. Obviously, the fluid reacts to that interaction changing its velocity in a highly nontrivial way. These fluid-solid interactions can be described mathematically as free boundary problems, i.e. PDEs where the spatial domain is also an unknown to be solved for. Another topic where free boundary problems arise is tumor growth. There, the boundary of a carcinoma immersed in healthy tissue can be thought as a free boundary problem for a system of PDEs that resembles the motion of a multiphase flow in porous media.

The goal of this workshop is to bring together mathematicians working in free boundary problems and biologists and engineers studying these type of fluid-solid interactions to enhance the possibilities of fruitful collaboration.