Forward invariance and Wong-Zakai approximation for stochastic moving boundary problems
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
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.
Details
Original language | English |
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Pages (from-to) | 869-929 |
Number of pages | 61 |
Journal | Journal of evolution equations |
Volume | 20 |
Issue number | 3 |
Publication status | Published - Sept 2020 |
Peer-reviewed | Yes |
External IDs
Scopus | 85074940112 |
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ORCID | /0000-0003-0913-3363/work/166762744 |
Keywords
Keywords
- Stochastic partial differential equation, Stefan problem, moving boundary problem, Phase separation, Forward invariance, Wong-Zakai approximation, EVOLUTION-EQUATIONS, EXISTENCE