PDE Real Analysis Seminar

Seminar information archive ~04/13Next seminarFuture seminars 04/14~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)


10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Juergen Saal (TU Darmstadt)
Analyticity of the interface of the classical two-phase Stefan problem
[ Abstract ]
The Stefan problem is a model for phase transitions in liquid-solid systems, as e.g. ice surrounded by water, and accounts for heat diffusion and exchange of latent heat in a homogeneous medium.
The strong formulation of this 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 the initial data the two-phase classical Stefan problem admits a unique solution that is analytic in space and time.
The result is based on $L_p$ maximal regularity for a linearized problem, which is proved first, and the implicit function theorem.
[ Reference URL ]