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Broadwell Model and Conservative Supersonic Boundary

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Abstract

In this paper, we consider an initial-boundary value problem for the Broadwell model with a supersonic physical boundary. Here, we pose a conservative boundary condition which preserves the total number of particles. We show that the solution converges pointwise to a boundary layer exponentially, when the perturbations of the initial data to the equilibrium state are sufficiently small, by using Green’s function as established in Lan et al. (Netw Heterog Media 1:167–183, 2006), weighted energy estimates and by constructing a pair of anti-derivatives to convert the conservative boundary condition into a dissipative boundary condition with conservation laws together with an a priori chosen boundary layer.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

    Shijin Deng & Weike Wang

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Shih-Hsien Yu

Authors
  1. Shijin Deng
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  2. Weike Wang
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  3. Shih-Hsien Yu
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Correspondence to Shih-Hsien Yu.

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Communicated by T.-P. Liu

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Deng, S., Wang, W. & Yu, SH. Broadwell Model and Conservative Supersonic Boundary. Arch Rational Mech Anal 200, 203–223 (2011). https://doi.org/10.1007/s00205-010-0344-4

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  • DOI: https://doi.org/10.1007/s00205-010-0344-4

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