### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*61*(9), 1298-1329. https://doi.org/10.1002/cpa.20256

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 61, no. 9, pp. 1298-1329. https://doi.org/10.1002/cpa.20256

}

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

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 -