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Behavior of the solution of a random semilinear heat equation
Author(s) -
Varadhan S. R. S.,
Zygouras Nikos
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20256
Subject(s) - mathematics , infinity , dimension (graph theory) , heat equation , space (punctuation) , steady state (chemistry) , mathematical analysis , variable (mathematics) , state space , pure mathematics , statistics , philosophy , linguistics , chemistry
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.