Forward invariance and Wong–Zakai approximation for stochastic moving boundary problems

@article{KellerRessel2019ForwardIA,
  title={Forward invariance and Wong–Zakai approximation for stochastic moving boundary problems},
  author={Martin Keller-Ressel and Marvin S. Mueller},
  journal={Journal of Evolution Equations},
  year={2019}
}
We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that proper separation of phases is attained, i.e., the solution remains negative on one side and positive on the other side of the moving interface, when started with the appropriate initial conditions. To extend results from deterministic settings to the stochastic case, we establish a Wong-Zakai type approximation. After a… 
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ON THE RELATION BETWEEN ORDINARY AND STOCHASTIC DIFFERENTIAL EQUATIONS
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