# American Institute of Mathematical Sciences

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August  2019, 24(8): 4317-4339. doi: 10.3934/dcdsb.2019121

## Approximation of the interface condition for stochastic Stefan-type problems

 ETH Zürich, Department of Mathematics, Rämistrasse 101, 8092 Zürich, Switzerland

Dedicated to Professor Peter E. Kloeden on the occasion of his 70th birthday

Received  March 2018 Revised  October 2018 Published  June 2019

Fund Project: The author acknowledges support by the Swiss National Science Foundation through grant SNF 205121 163425

We consider approximations of the Stefan-type condition by imbalances of volume closely around the inner interface and study convergence of the solutions of the corresponding semilinear stochastic moving boundary problems. After a coordinate transformation, the problems can be reformulated as stochastic evolution equations on fractional power domains of linear operators. Here, the coefficients might fail to have linear growths and might be Lipschitz continuous only on bounded sets. We show continuity properties of the mild solution map in the coefficients and initial data, also incorporating the possibility of explosion of the solutions.

Citation: Marvin S. Müller. Approximation of the interface condition for stochastic Stefan-type problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4317-4339. doi: 10.3934/dcdsb.2019121
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