An asymptotic theory for randomly forced discrete nonlinear heat equations

Mohammud Foondun, Davar Khoshnevisan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study discrete nonlinear parabolic stochastic heat equations of the form, un+1(x)-un(x) = (Lun)(x)+ σ(u n(x))ζn(x), for n ∈ Z+ and x ∈ Zd, where ζ := {ζn(x)} n≥0,x∈Zd denotes 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.

LanguageEnglish
Pages1042-1060
Number of pages19
JournalBernoulli
Volume18
Issue number3
Early online date28 Jun 2012
DOIs
Publication statusPublished - 31 Aug 2012
Externally publishedYes

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Nonlinear Heat Equation
Asymptotic Theory
Stochastic PDEs
Stochastic Heat Equation
Comparison Principle
Unique Solution
Forcing
Random walk
Generator
Denote
Form

Keywords

  • intermittency
  • stochastic heat equations

Cite this

Foondun, Mohammud ; Khoshnevisan, Davar. / An asymptotic theory for randomly forced discrete nonlinear heat equations. In: Bernoulli. 2012 ; Vol. 18, No. 3. pp. 1042-1060.
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An asymptotic theory for randomly forced discrete nonlinear heat equations. / Foondun, Mohammud; Khoshnevisan, Davar.

In: Bernoulli, Vol. 18, No. 3, 31.08.2012, p. 1042-1060.

Research output: Contribution to journalArticle

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