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 language | English (US) |
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Pages (from-to) | 1298-1329 |
Number of pages | 32 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 61 |
Issue number | 9 |
DOIs | |
State | Published - Sep 2008 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
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
}
TY - JOUR
T1 - Behavior of the solution of a random semilinear heat equation
AU - Varadhan, S. R S
AU - Zygouras, Nikos
PY - 2008/9
Y1 - 2008/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=52349100647&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=52349100647&partnerID=8YFLogxK
U2 - 10.1002/cpa.20256
DO - 10.1002/cpa.20256
M3 - Article
AN - SCOPUS:52349100647
VL - 61
SP - 1298
EP - 1329
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 9
ER -