Author
Hambly, B
Kalsi, J
Journal title
Stochastic Processes and their Applications
DOI
10.1016/j.spa.2019.04.003
Issue
2
Volume
130
Last updated
2024-03-23T10:34:11.64+00:00
Page
924-961
Abstract
We prove the existence and uniqueness of solutions to a one-dimensional Stefan Problem for reflected SPDEs which are driven by space–time white noise. The solutions are shown to exist until almost surely positive blow-up times. Such equations can model the evolution of phases driven by competition at an interface, with the dynamics of the shared boundary depending on the derivatives of two competing profiles at this point. The novel features here are the presence of space–time white noise; the reflection measures, which maintain positivity for the competing profiles; and a sufficient condition to make sense of the Stefan condition at the boundary. We illustrate the behaviour of the solution numerically to show that this sufficient condition is close to necessary.
Symplectic ID
987810
Favourite
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Publication type
Journal Article
Publication date
10 Apr 2019
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