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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 (engelsk)Inngår i: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 130, nr 9, s. 5605-5635Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2020. Vol. 130, nr 9, s. 5605-5635
Emneord [en]
Non-local, Stochastic partial differential equations, Strong positivity, Hopf’s lemma, Blow-up, Exponential Brownian functionals
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
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
Tilgjengelig fra: 2022-02-17 Laget: 2022-02-17 Sist oppdatert: 2022-02-17bibliografisk kontrollert

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Kavallaris, Nikos I.

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