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A boundedness trichotomy for the stochastic heat equation SCIE SCOPUS

Title
A boundedness trichotomy for the stochastic heat equation
Authors
Chen, LeKhoshnevisan, DavarKim, Kunwoo
Date Issued
2017-11
Publisher
INST MATHEMATICAL STATISTICS
Abstract
We consider the stochastic heat equation with a multiplicative white noise forcing term under standard " intermitency conditions." The main finding of this paper is that, under mild regularity hypotheses, the a. s.-boundedness of the solution x bar right arrow u(t, x) can be characterized generically by the decay rate, at +/-infinity, of the initial function u(0). More specifically, we prove that there are 3 generic boundedness regimes, depending on the numerical value of Lambda := lim(|x|->infinity) | log u(0)(x)|/(log | x|)(2/3).
URI
https://oasis.postech.ac.kr/handle/2014.oak/50747
DOI
10.1214/16-AIHP780
ISSN
0246-0203
Article Type
Article
Citation
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, vol. 53, no. 4, page. 1991 - 2004, 2017-11
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김건우KIM, KUNWOO
Dept of Mathematics
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