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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; th...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.spa.2019.04.003

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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 Publisher's website
Journal:
Stochastic Processes and their Applications Journal website
Volume:
130
Issue:
2
Pages:
924-961
Publication date:
2019-04-10
Acceptance date:
2019-04-01
DOI:
ISSN:
0304-4149
Source identifiers:
987810
Language:
English
Pubs id:
pubs:987810
UUID:
uuid:44d52803-aa68-4cf7-b0db-82e5034d087f
Local pid:
pubs:987810
Deposit date:
2019-04-10

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