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Finite-time blow-up of a non-local stoch...
Kavallaris, Nikos I....

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Finite-time blow-up of a non-local stochastic parabolic problem by Kavallaris, Nikos I. ( Author )
Lemonjar Open Access
N.A
01-01-2015
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.
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English
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MYR 0.00
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http://arxiv.org/abs/1508.05496
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