Characteristic half space problem for the Broadwell model

  • Received: 01 July 2013 Revised: 01 August 2013
  • Primary: 82C40.

  • We study an initial boundary value problem for the Broadwell model in half space. The Green's function for the initial boundary value problem is decomposed into two parts: one is the Green's function for the initial value problem, we call it the fundamental solution for the whole space; the other is the convolution of this fundamental solution with full boundary data. A new approach to obtain the full boundary data is established here. Finally, a nonlinear time-asymptotic stability of an equilibrium state is proved.

    Citation: Linglong Du. Characteristic half space problem for the Broadwell model[J]. Networks and Heterogeneous Media, 2014, 9(1): 97-110. doi: 10.3934/nhm.2014.9.97

    Related Papers:

    [1] Linglong Du . Characteristic half space problem for the Broadwell model. Networks and Heterogeneous Media, 2014, 9(1): 97-110. doi: 10.3934/nhm.2014.9.97
    [2] Chiu-Ya Lan, Huey-Er Lin, Shih-Hsien Yu . The Green's functions for the Broadwell Model in a half space problem. Networks and Heterogeneous Media, 2006, 1(1): 167-183. doi: 10.3934/nhm.2006.1.167
    [3] Shijin Deng, Weike Wang, Shih-Hsien Yu . Pointwise convergence to a Maxwellian for a Broadwell model with a supersonic boundary. Networks and Heterogeneous Media, 2007, 2(3): 383-395. doi: 10.3934/nhm.2007.2.383
    [4] Alberto Bressan, Khai T. Nguyen . Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10(2): 255-293. doi: 10.3934/nhm.2015.10.255
    [5] Alessia Marigo . Optimal traffic distribution and priority coefficients for telecommunication networks. Networks and Heterogeneous Media, 2006, 1(2): 315-336. doi: 10.3934/nhm.2006.1.315
    [6] Tong Li, Nitesh Mathur . Global well-posedness and asymptotic behavior of $ BV $ solutions to a system of balance laws arising in traffic flow. Networks and Heterogeneous Media, 2023, 18(2): 581-600. doi: 10.3934/nhm.2023025
    [7] Mauro Garavello . A review of conservation laws on networks. Networks and Heterogeneous Media, 2010, 5(3): 565-581. doi: 10.3934/nhm.2010.5.565
    [8] Jan Friedrich, Simone Göttlich, Annika Uphoff . Conservation laws with discontinuous flux function on networks: a splitting algorithm. Networks and Heterogeneous Media, 2023, 18(1): 1-28. doi: 10.3934/nhm.2023001
    [9] Linglong Du, Min Yang . Pointwise long time behavior for the mixed damped nonlinear wave equation in $ \mathbb{R}^n_+ $. Networks and Heterogeneous Media, 2021, 16(1): 49-67. doi: 10.3934/nhm.2020033
    [10] Anya Désilles . Viability approach to Hamilton-Jacobi-Moskowitz problem involving variable regulation parameters. Networks and Heterogeneous Media, 2013, 8(3): 707-726. doi: 10.3934/nhm.2013.8.707
  • We study an initial boundary value problem for the Broadwell model in half space. The Green's function for the initial boundary value problem is decomposed into two parts: one is the Green's function for the initial value problem, we call it the fundamental solution for the whole space; the other is the convolution of this fundamental solution with full boundary data. A new approach to obtain the full boundary data is established here. Finally, a nonlinear time-asymptotic stability of an equilibrium state is proved.


    [1] S.-J. Deng, W.-K. Wang and S.-H. Yu, Pointwise convergence to a Maxwellian for a Broadwellw model with a supersonic boundary, Netw. Heterog. Media, 2 (2007), 383-395. doi: 10.3934/nhm.2007.2.383
    [2] C.-Y. Lan, H.-E. Lin and S.-H. Yu, The Green's functions for the Broadwell model in a half space problem, Netw. Heterog. Media, 1 (2006), 167-183. doi: 10.3934/nhm.2006.1.167
    [3] C.-Y. Lan, H.-E. Lin and S.-H. Yu, The Green's functions for the Broadwell model with a transonic boundary, J. Hyperbolic Differ. Equ., 5 (2008), 279-294. doi: 10.1142/S0219891608001489
    [4] T.-P. Liu, Pointwise convergence to shock waves for viscous conservarion laws, Commun. Pure Appl. Math., 50 (1997), 1113-1182. doi: 10.1002/(SICI)1097-0312(199711)50:11<1113::AID-CPA3>3.0.CO;2-D
    [5] T.-P. Liu and S.-H. Yu, Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation, Commun. Pure Appl. Math., 60 (2007), 295-356. doi: 10.1002/cpa.20172
    [6] T.-P. Liu and S.-H. Yu, On boundary relation for some dissipative systems, Bull. Inst. Math. Acad. Sin. (N.S.), 6 (2011), 245-267.
    [7] Y. Sone, Kinetic Theory and Fluid Dynamics, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2002. doi: 10.1007/978-1-4612-0061-1
  • This article has been cited by:

    1. Linglong Du, Splitting scheme for the stability of strong shock profile, 2016, 261, 00220396, 4055, 10.1016/j.jde.2016.06.018
  • Reader Comments
  • © 2014 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3303) PDF downloads(74) Cited by(1)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog