PDE Seminar Analytic solutions for the classical Stefan problem
 Date

20060217 16:30 
20060217 17:30
 Place
 Faculty of Science Building #8 Room 309

Speaker/Organizer
 Juergen Saal (TU Darmstadt)

 The Stefan problem is a model for phase transitionsin liquidsolid 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 twophase 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.
http://coe.math.sci.hokudai.ac.jp/sympo/pde/index_en.html