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Networks and Heterogeneous Media

2007, Volume 2, Issue 3: 383-395. doi: 10.3934/nhm.2007.2.383
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Pointwise convergence to a Maxwellian for a Broadwell model with a supersonic boundary

  • 1.
    Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai
  • 2.
    Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong
  • Received: 01 March 2007 Revised: 01 May 2007

  • Primary: 82C40.

  • In this paper, we consider an initial-boundary value problem for the Broadwell model with a supersonic physical boundary. By using the Green’s function established in [6] and weighted energy estimates, we show that the solution converges pointwise to the equilibrium state when the perturbations are sufficiently small.

    Citation: Shijin Deng, Weike Wang, Shih-Hsien Yu. Pointwise convergence to a Maxwellian for a Broadwell model with a supersonic boundary[J]. Networks and Heterogeneous Media, 2007, 2(3): 383-395. doi: 10.3934/nhm.2007.2.383

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  • In this paper, we consider an initial-boundary value problem for the Broadwell model with a supersonic physical boundary. By using the Green’s function established in [6] and weighted energy estimates, we show that the solution converges pointwise to the equilibrium state when the perturbations are sufficiently small.


  • This article has been cited by:

    1. Shijin Deng, Weike Wang, Shih-Hsien Yu, Broadwell Model and Conservative Supersonic Boundary, 2011, 200, 0003-9527, 203, 10.1007/s00205-010-0344-4
    2. HUEY-ER LIN, NONLINEAR STABILITY OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE BROADWELL MODEL AROUND A MAXWELLIAN, 2011, 08, 0219-8916, 131, 10.1142/S0219891611002354
    3. Linglong Du, Characteristic half space problem for the Broadwell model, 2014, 9, 1556-181X, 97, 10.3934/nhm.2014.9.97
    4. Niclas Bernhoff, Boundary Layers and Shock Profiles for the Broadwell Model, 2016, 2016, 1687-9643, 1, 10.1155/2016/5801728
    5. Shijin Deng, Weike Wang, The Broadwell model with a subsonic boundary, 2008, 69, 0362546X, 3849, 10.1016/j.na.2007.10.020
    6. Shijin Deng, Linglong Du, Shih-Hsien Yu, Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition, 2013, 6, 1937-5077, 865, 10.3934/krm.2013.6.865
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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