Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • apa.csl
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Finite-time blow-up of a non-local stochastic parabolic problem
University of Chester, GBR.ORCID iD: 0000-0002-9743-8636
University of Chester, GBR.
2020 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 130, no 9, p. 5605-5635Article in journal (Refereed) Published
Abstract [en]

The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existence and uniqueness of the local-in-time weak solution for such problem. The first part of the manuscript deals with the investigation of the conditions which guarantee the occurrence of noise-induced blow-up. In the second part we first prove the C1-spatial regularity of the solution. Then, based on this regularity result, and using a strong positivity result we derive, for first in the literature of SPDEs, a Hopf’s type boundary value point lemma. The preceding results together with Kaplan’s eigenfunction method are then employed to provide a (non-local) drift term induced blow-up result. In the last part of the paper, we present a method which provides an upper bound of the probability of (non-local) drift term induced blow-up.

Place, publisher, year, edition, pages
2020. Vol. 130, no 9, p. 5605-5635
Keywords [en]
Non-local, Stochastic partial differential equations, Strong positivity, Hopf’s lemma, Blow-up, Exponential Brownian functionals
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-88606DOI: 10.1016/j.spa.2020.04.002ISI: 000553446700014Scopus ID: 2-s2.0-85083464823OAI: oai:DiVA.org:kau-88606DiVA, id: diva2:1638711
Available from: 2022-02-17 Created: 2022-02-17 Last updated: 2022-02-17Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records

Kavallaris, Nikos I.

Search in DiVA

By author/editor
Kavallaris, Nikos I.
In the same journal
Stochastic Processes and their Applications
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 98 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • apa.csl
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf