White noise perturbation of the viscous shock fronts of the Burgers equation

Jan Wehr Jack Xin

Analysis of PDEs mathscidoc:1912.43863

Communications in mathematical physics, 181, (1), 183-203, 1996.11
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<i>t</i>, as<i>t</i> goes to infinity. With probability arbitrarily close to one, the front width is<i>O</i>(1) for large time.
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@inproceedings{jan1996white,
  title={White noise perturbation of the viscous shock fronts of the Burgers equation},
  author={Jan Wehr, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210301906076427},
  booktitle={Communications in mathematical physics},
  volume={181},
  number={1},
  pages={183-203},
  year={1996},
}
Jan Wehr, and Jack Xin. White noise perturbation of the viscous shock fronts of the Burgers equation. 1996. Vol. 181. In Communications in mathematical physics. pp.183-203. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210301906076427.
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