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

  • Martin Keller-Ressel
  • Marvin S. MüllerEmail author


We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly nonlinear, 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 coordinate transformation, the problems are reformulated and analyzed in terms of stochastic evolution equations on domains of fractional powers of linear operators.


Stochastic partial differential equation Stefan problem moving boundary problem Phase separation Forward invariance Wong–Zakai approximation 

Mathematics Subject Classification

60H15 35R60 



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Authors and Affiliations

  1. 1.Department of Mathematical StochasticTU DresdenDresdenGermany
  2. 2.Department of MathematicsETH ZürichZurichSwitzerland
  3. 3.Zenai AGZurichSwitzerland

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