A Gradient Flow Approach for Dissipative Equations on a Free Domain

摘要

We describe the construction of solutions of a problem consisting of a free boundary problem describing the swelling of a cell by osmosis. The problem consists of diffusion, a zero-flux boundary condition and movement of the boundary by surface tension and osmotic pressure. The method of construction is derived from methods used to construct gradient flows. Finally, we describe difficulties that arise when diffusion is replaced by a more general parabolic PDE.