Free boundary problems describing fluid accumulation in thin-film flows driven by surface tension and gravity

In this talk I will describe some free boundaries arising in the description of regions where the motion of thin fluid layers becomes slow. These regions are often characterized by the onset of oscillations in the in the interfaces. Classical examples include the description of fluid layers attached to a moving wall. I will describe the free boundary problem arising in the description of the regions where a liquid moving in a bumpy interface accumulates. In the two-dimensional case, this problem reduces to a boundary value problem for a fourth order ordinary differential equation whose solution can be obtained using methods of dynamical systems.

(Joint work with C. Cuesta).