| Abstract: |
| We extend an article by Hilhorst, Mimura and Schatzle
about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem
arising in biology. We introduce a one-dimensional additive white noise in time,
and search for the limit of the solution of the corresponding stochastic Stefan problem
as the latent heat coefficient vanishes. We first prove the existence and uniqueness
of the weak solution of this problem, and then study the limit of the solution as the
latent heat coefficient tends to zero. Our method of proof is based upon
an error estimate between the solution of the Stefan problem with positive latent heat
and the one of the Stefan problem with zero latent heat, which seems to be novel even in
the deterministic case when no noise is added. |
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