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Stefan problems for reflected SPDEs driven by space-time white noise

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.spa.2019.04.003

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Anne's College
Role:
Author
ORCID:
0000-0003-0086-0695


Publisher:
Elsevier
Journal:
Stochastic Processes and their Applications More from this journal
Volume:
130
Issue:
2
Pages:
924-961
Publication date:
2019-04-10
Acceptance date:
2019-04-01
DOI:
ISSN:
0304-4149


Language:
English
Pubs id:
pubs:987810
UUID:
uuid:44d52803-aa68-4cf7-b0db-82e5034d087f
Local pid:
pubs:987810
Source identifiers:
987810
Deposit date:
2019-04-10

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