Behavior of the solution of a random semilinear heat equation

S. R S Varadhan, Nikos Zygouras

Research output: Contribution to journal › Article

Abstract

We consider a semilinear heat equation in one space dimension, with a random source at the origin. We study the solution, which describes the equilibrium of this system, and prove that, as the space variable tends to infinity, the solution becomes a.s. asymptotic to a steady state. We also study the fluctuations of the solution around the steady state.

Original languageEnglish (US)
Pages (from-to)1298-1329
Number of pages32
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number9
DOIs
StatePublished - Sep 2008

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Semilinear Heat Equation
Infinity
Tend
Fluctuations
Hot Temperature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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Behavior of the solution of a random semilinear heat equation. / Varadhan, S. R S; Zygouras, Nikos.

In: Communications on Pure and Applied Mathematics, Vol. 61, No. 9, 09.2008, p. 1298-1329.

Research output: Contribution to journal › Article

Varadhan, SRS & Zygouras, N 2008, 'Behavior of the solution of a random semilinear heat equation', Communications on Pure and Applied Mathematics, vol. 61, no. 9, pp. 1298-1329. https://doi.org/10.1002/cpa.20256
Varadhan SRS, Zygouras N. Behavior of the solution of a random semilinear heat equation. Communications on Pure and Applied Mathematics. 2008 Sep;61(9):1298-1329. https://doi.org/10.1002/cpa.20256
Varadhan, S. R S ; Zygouras, Nikos. / Behavior of the solution of a random semilinear heat equation. In: Communications on Pure and Applied Mathematics. 2008 ; Vol. 61, No. 9. pp. 1298-1329.
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