Abstract

The purpose of this talk is to extend an article by Hilhorst, Mimura and Schätzle [1] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We now introduce an additive noise term, so that we have to deal with a rather simple case of a stochastic partial differential equation. Some ideas for the proof are partly inspired from an article of Vallet [2] but they involve a slightly different notion of solution. Unlike in [1], our method of proof is based upon an error estimate, which seems to be novel even in the deterministic case when no noise is added.
 

References

[1] Danielle Hilhorst, Masayasu Mimura, and Reiner Schätzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Anal., Real World Appl. 4, No. 2, (2003) 261-285.

[2] Guy Vallet, Stochastic perturbation of nonlinear degenerate parabolic problems, Differ. Integral Equ. 21, No. 11-12, (2008) 1055-1082.
 

Organizer: Chun-Hsiung Hsia (NTU)