Abstract. We study discrete nonlinear parabolic stochastic heat equations of the form un+1(x) - un (x) = Lun + σ(un(x))ξn(x), for positive integers n and x in Zd, where the ξ's denote random forcing and L the generator of a random walk on Zd. Under mild conditions, we prove that the preceding stochastic PDE has a unique solution that grows at most exponentially in time. And that, under natural conditions, it is "weakly intermittent." Along the way, we establish a comparison principle as well as a finite-support property.
Keywords. Stochastic heat equation, intermittency.
AMS Classification (2000). Primary. 35R60, 37H10, 60H15; Secondary. 82B44.
Support. The research of DK was supported in part by a grant from the U.S. National Science Foundation.
Pre/E-Prints. This paper is available in
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Mohammud Foondun Department of Mathematics University of Utah 155 S, 1400 E JWB 233 Salt Lake City, UT 84112-0090, U.S.A. mohammud@math.utah.edu |
Davar Khoshnevisan Department of Mathematics University of Utah 155 S, 1400 E JWB 233 Salt Lake City, UT 84112-0090, U.S.A. davar@math.utah.edu |
Last Update: November 5, 2008
©
2008 - Mohammud Foondun and Davar Khoshnevisan