Free boundary problems, are understood as partial differential equations, where the form of the boundary is part of the solution. One classical example is a piece of ice which is melting in water. Here the border between ice and water can be seen as part of the solution.
The thesis should investigate the model of ice melting in water, known as the Stefan Problem. It is a parabolic free boundary problem. The task will be to investigate qualitative problems of the free boundary. Especially to understand the smoothing effects when time is increasing.
Seznam odborné literatury
Avner Friedman: Variational Principles and Free-Boundary problems, John Wiley & Sons, Inc. (1982)
Předběžná náplň práce v anglickém jazyce
This master thesis can be extended to a PhD thesis, where kinetic effects would be taken into account. This will be achieved by coupling the free boundary problem with the Navier Stokes equation, that describes the flow of liquids.
