Math @ Duke

Publications [#246848] of JianGuo Liu
Papers Published
 Coquel, F; Jin, S; Liu, JG; Wang, L, WellPosedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a TwoScale Discontinuous Relaxation Rate,
Archive for Rational Mechanics and Analysis, vol. 214 no. 3
(January, 2014),
pp. 10511084, ISSN 00039527 [doi]
(last updated on 2018/12/14)
Abstract: © 2014, SpringerVerlag Berlin Heidelberg. 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 twoscale 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 wellposedness 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 twoscale problem originally proposed in Jin et al. in Math. Comp. 82, 749–779, 2013.


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