PDE Seminar Analytic solutions for the classical Stefan problem

2006-02-17 16:30 - 2006-02-17 17:30
Faculty of Science Building #8 Room 309
Juergen Saal (TU Darmstadt)
The Stefan problem is a model for phase transitionsin liquid-solid systems, as e.g. ice surrounded by water,and accounts for heat diffusion and exchange of latentheat in a homogeneous medium. The strong formulation ofthis model corresponds to a free boundary problem involving a parabolic diffusion equation for each phase and a transmission condition prescribed at the interface separating the phases.We prove that under mild regularity assumptions on theinitial data the two-phase classical Stefan problem admitsa unique solution that is analytic in space and time.The result is based on $L_p$ maximal regularity for alinearized problem, which is proved first, and the implicit function theorem.