Project Joachim Escher

The objective of our project is to mathematically investigate multi-dimensional moving boundary problems describing the deformation of semipermeable membranes separating two liquid phases. These models have been primarily discussed in a biomathematical context where osmotic swelling of cells has been investigated. The mathematical structure behind these models is given by nonlinear dynamical systems with infinitely many degrees of freedom. Significant progress in linear and nonlinear analysis in the past three decades allows to treat the full multi-dimensional problem and to address questions like well-posedness of the mathematical model, stability and bifurcation properties of steady states, as well as determining possible blow-up mechanisms.