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arXiv.org e-Print Archive
Preprint . 2019
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2019
License: arXiv Non-Exclusive Distribution
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Global existence and non-existence of stochastic parabolic equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2019Embargo end date: 01 Jan 2019Publisher:arXiv
Authors: Lv, Guangying; Wei, Jinlong;

doi: 10.48550/arxiv.1902.07389

arXiv: 1902.07389

Global existence and non-existence of stochastic parabolic equations

Abstract

This paper is concerned with the blowup phenomenon of stochastic parabolic equations both on bounded domain and in the whole space. We introduce a new method to study the blowup phenomenon on bounded domain. Comparing with the existing results, we delete the assumption that the solutions to stochastic heat equations are non-negative. Then the blowup phenomenon in the whole space is obtained by using the properties of heat kernel. We obtain that the solutions will blow up in finite time for nontrivial initial data.

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Keywords

Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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