Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate

Coquel, Frédéric 1, École Polytechnique, Route de Saclay Shi Jin University of Wisconsin-Madison Jian-Guo Liu Duke University Li Wang University of Michigan

Analysis of PDEs mathscidoc:1702.03032

Archive for Rational Mechanics and Analysis, 214, (3), 1051–1084, 2014.12
Nonlinear hyperbolic systems with relaxations may encounter different scales of relaxation time, which is a prototype multiscale phenomenon that arises in many applications. In such a problem the relaxation time is of O(1) in part of the domain and very small in the remaining domain in which the solution can be approximated by the zero relaxation limit which can be solved numerically much more efficiently. For the Jin–Xin relaxation system in such a two-scale setting, we establish its wellposedness and singular limit as the (smaller) relaxation time goes to zero. The limit is a multiscale coupling problem which couples the original Jin–Xin system on the domain when the relaxation time is O(1) with its relaxation limit in the other domain through interface conditions which can be derived by matched interface layer analysis.As a result, we also establish the well-posedness and regularity (such as boundedness in sup norm with bounded total variation and L 1-contraction) of the coupling problem, thus providing a rigorous mathematical foundation, in the general nonlinear setting, to the multiscale domain decomposition method for this two-scale problem originally proposed in Jin et al. in Math. Comp. 82, 749–779, 2013.
No keywords uploaded!
[ Download ] [ 2017-02-08 00:04:02 uploaded by jianguo ] [ 666 downloads ] [ 0 comments ]
@inproceedings{coquel,2014well-posedness,
  title={Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate},
  author={Coquel, Frédéric, Shi Jin, Jian-Guo Liu, and Li Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208000402889514289},
  booktitle={Archive for Rational Mechanics and Analysis},
  volume={214},
  number={3},
  pages={1051–1084},
  year={2014},
}
Coquel, Frédéric, Shi Jin, Jian-Guo Liu, and Li Wang. Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate. 2014. Vol. 214. In Archive for Rational Mechanics and Analysis. pp.1051–1084. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208000402889514289.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved