Finite-time blow-up of a non-local stochastic parabolic problem

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Kavallaris, Nikos, I¹  Yan, Yubin¹ 

[1] Univ Chester, Sch Sci & Engn, Dept Math & Phys Sci, Thornton Sci Pk Pool Lane, Chester CH2 4NU, Cheshire, England

关键词: Non-local;    Stochastic partial differential equations;    Strong positivity;    Hopf's lemma;    Blow-up;    Exponential Brownian functionals;   

DOI  :  10.1016/j.spa.2020.04.002

来源: Elsevier

【 摘 要 】

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 C-1-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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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