### Abstract

We study the front dynamics of solutions of the initial value problem of the Burgers equation with initial data being the viscous shock front plus the white noise perturbation. In the sense of distribution, the solutions propagate with the same speed as the unperturbed front, however, the front location is random and satisfies a central limit theorem with the variance proportional to the time t, as t goes to infinity. With probability arbitrarily close to one, the front width is O(1) for large time.

Original language | English (US) |
---|---|

Pages (from-to) | 183-203 |

Number of pages | 21 |

Journal | Communications in Mathematical Physics |

Volume | 181 |

Issue number | 1 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*181*(1), 183-203.

**White noise perturbation of the viscous shock fronts of the burgers equation.** / Wehr, Jan; Xin, J.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 181, no. 1, pp. 183-203.

}

TY - JOUR

T1 - White noise perturbation of the viscous shock fronts of the burgers equation

AU - Wehr, Jan

AU - Xin, J.

PY - 1996

Y1 - 1996

N2 - We study the front dynamics of solutions of the initial value problem of the Burgers equation with initial data being the viscous shock front plus the white noise perturbation. In the sense of distribution, the solutions propagate with the same speed as the unperturbed front, however, the front location is random and satisfies a central limit theorem with the variance proportional to the time t, as t goes to infinity. With probability arbitrarily close to one, the front width is O(1) for large time.

AB - We study the front dynamics of solutions of the initial value problem of the Burgers equation with initial data being the viscous shock front plus the white noise perturbation. In the sense of distribution, the solutions propagate with the same speed as the unperturbed front, however, the front location is random and satisfies a central limit theorem with the variance proportional to the time t, as t goes to infinity. With probability arbitrarily close to one, the front width is O(1) for large time.

UR - http://www.scopus.com/inward/record.url?scp=0002251023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002251023&partnerID=8YFLogxK

M3 - Article

VL - 181

SP - 183

EP - 203

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -