We consider a stochastic perturbation of the Stefan problem. The noise is Brownian in time and smoothly correlated in space. We prove existence and uniqueness and characterize the domain of existence.
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This work was supported by NSF grant DMS0705260. R.S. would like to thanks the Departments of Mathematics and Statistics of Stanford University for their hospitality in the Spring of 2010 during a sabbatical stay. The authors would like to thank the anonymous referee for his meticulous reading of the original version of this manuscript.
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Kim, K., Zheng, Z. & Sowers, R.B. A Stochastic Stefan Problem. J Theor Probab 25, 1040–1080 (2012). https://doi.org/10.1007/s10959-011-0392-1
- Stochastic partial differential equations
- Stefan boundary condition
- Spatially correlated noise
Mathematics Subject Classification (2000)