Journal article
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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- Files:
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(Preview, Accepted manuscript, pdf, 890.0KB, Terms of use)
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- Publisher copy:
- 10.1016/j.spa.2019.04.003
Authors
- 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:
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0304-4149
- Language:
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English
- Pubs id:
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pubs:987810
- UUID:
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uuid:44d52803-aa68-4cf7-b0db-82e5034d087f
- Local pid:
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pubs:987810
- Source identifiers:
-
987810
- Deposit date:
-
2019-04-10
Terms of use
- Copyright holder:
- Elsevier B.V.
- Copyright date:
- 2019
- Rights statement:
- © 2019 Elsevier B.V. All rights reserved.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Elsevier at: https://doi.org/10.1016/j.spa.2019.04.003
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