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Networks and Heterogeneous Media

2006, Volume 1, Issue 1: 167-183. doi: 10.3934/nhm.2006.1.167
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The Green's functions for the Broadwell Model in a half space problem

  • 1.
    Department of Applied Mathematics, National Sun Yet-sen University, Kaohsiung
  • 2.
    Department of Mathematics, National Taiwan Normal University, Taipei
  • 3.
    Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong
  • Received: 01 September 2005 Revised: 01 November 2005

  • Primary: 82C40.

  • We study an initial boundary value problem for the Broadwell model with a supersonic physical boundary. The Green's function for an initial value problem is constructed and its detailed pointwise structure is obtained through the novel decompositions introduced in [8]. With the Green's function for initial value problem and energy estimates together, a new approach to convert a priori L2-boundary data into L∞ boundary data is established for the Broadwell model. The Green's function for an initial boundary value problem is obtained. Finally, a nonlinearly time-asymptotic stability of an equilibrium state is proved.

    Citation: Chiu-Ya Lan, Huey-Er Lin, Shih-Hsien Yu. The Green's functions for the Broadwell Model in a half space problem[J]. Networks and Heterogeneous Media, 2006, 1(1): 167-183. doi: 10.3934/nhm.2006.1.167

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  • We study an initial boundary value problem for the Broadwell model with a supersonic physical boundary. The Green's function for an initial value problem is constructed and its detailed pointwise structure is obtained through the novel decompositions introduced in [8]. With the Green's function for initial value problem and energy estimates together, a new approach to convert a priori L2-boundary data into L∞ boundary data is established for the Broadwell model. The Green's function for an initial boundary value problem is obtained. Finally, a nonlinearly time-asymptotic stability of an equilibrium state is proved.


  • 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. CHIU-YA LAN, HUEY-ER LIN, SHIH-HSIEN YU, THE GREEN'S FUNCTION FOR THE BROADWELL MODEL WITH A TRANSONIC BOUNDARY, 2008, 05, 0219-8916, 279, 10.1142/S0219891608001489
    3. Linglong Du, Characteristic half space problem for the Broadwell model, 2014, 9, 1556-181X, 97, 10.3934/nhm.2014.9.97
    4. ShiJin Deng, WeiKe Wang, Pointwise decaying rate of large perturbation around viscous shock for scalar viscous conservation law, 2013, 56, 1674-7283, 729, 10.1007/s11425-012-4566-9
    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, Weike Wang, Shih-Hsien Yu, Bifurcation on boundary data for linear broadwell model with conservative boundary condition, 2014, 11, 0219-8916, 603, 10.1142/S0219891614500179
    7. 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
    8. Niclas Bernhoff, Boundary Layers and Shock Profiles for the Broadwell Model, 2016, 2016, 1687-9643, 1, 10.1155/2016/5801728
    9. 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
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  • © 2006 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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