Scaling limits of waves in convex scalar conservation laws under random initial perturbations

Jan Wehr Jack Xin

Analysis of PDEs mathscidoc:1912.43913

Journal of statistical physics, 122, (2), 361-370, 2006.1
We study waves in convex scalar conservation laws under noisy initial perturbations. It is known that the building blocks of these waves are shock and rarefaction waves, both are invariant under hyperbolic scaling. Noisy perturbations can generate complicated wave patterns, such as diffusion process of shock locations. However we show that under the hyperbolic scaling, the solutions converge in the sense of distribution to the unperturbed waves. In particular, randomly perturbed shock waves move at the unperturbed velocity in the scaling limit. Analysis makes use of the Hopf formula of the related Hamilton-Jacobi equation and regularity estimates of noisy processes.
No keywords uploaded!
[ Download ] [ 2019-12-24 21:06:14 uploaded by Jack_Xin ] [ 208 downloads ] [ 0 comments ]
@inproceedings{jan2006scaling,
  title={Scaling limits of waves in convex scalar conservation laws under random initial perturbations},
  author={Jan Wehr, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210614511087477},
  booktitle={Journal of statistical physics},
  volume={122},
  number={2},
  pages={361-370},
  year={2006},
}
Jan Wehr, and Jack Xin. Scaling limits of waves in convex scalar conservation laws under random initial perturbations. 2006. Vol. 122. In Journal of statistical physics. pp.361-370. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210614511087477.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved