September  2007, 2(3): 383-395. doi: 10.3934/nhm.2007.2.383

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, China, China

2. 

Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong

Received  March 2007 Revised  May 2007 Published  June 2007

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. Networks & Heterogeneous Media, 2007, 2 (3) : 383-395. doi: 10.3934/nhm.2007.2.383
[1]

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

[2]

Wen-ming He, Jun-zhi Cui. The estimate of the multi-scale homogenization method for Green's function on Sobolev space $W^{1,q}(\Omega)$. Communications on Pure & Applied Analysis, 2012, 11 (2) : 501-516. doi: 10.3934/cpaa.2012.11.501

[3]

Shijin Deng, Linglong Du, Shih-Hsien Yu. Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition. Kinetic & Related Models, 2013, 6 (4) : 865-882. doi: 10.3934/krm.2013.6.865

[4]

Peter Bella, Arianna Giunti. Green's function for elliptic systems: Moment bounds. Networks & Heterogeneous Media, 2018, 13 (1) : 155-176. doi: 10.3934/nhm.2018007

[5]

Virginia Agostiniani, Rolando Magnanini. Symmetries in an overdetermined problem for the Green's function. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 791-800. doi: 10.3934/dcdss.2011.4.791

[6]

Sungwon Cho. Alternative proof for the existence of Green's function. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1307-1314. doi: 10.3934/cpaa.2011.10.1307

[7]

Margaret Beck. Stability of nonlinear waves: Pointwise estimates. Discrete & Continuous Dynamical Systems - S, 2017, 10 (2) : 191-211. doi: 10.3934/dcdss.2017010

[8]

Diego Castellaneta, Alberto Farina, Enrico Valdinoci. A pointwise gradient estimate for solutions of singular and degenerate pde's in possibly unbounded domains with nonnegative mean curvature. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1983-2003. doi: 10.3934/cpaa.2012.11.1983

[9]

Jeremiah Birrell. A posteriori error bounds for two point boundary value problems: A green's function approach. Journal of Computational Dynamics, 2015, 2 (2) : 143-164. doi: 10.3934/jcd.2015001

[10]

Li-Ming Yeh. Pointwise estimate for elliptic equations in periodic perforated domains. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1961-1986. doi: 10.3934/cpaa.2015.14.1961

[11]

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

[12]

Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems & Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487

[13]

Jongkeun Choi, Ki-Ahm Lee. The Green function for the Stokes system with measurable coefficients. Communications on Pure & Applied Analysis, 2017, 16 (6) : 1989-2022. doi: 10.3934/cpaa.2017098

[14]

Hideo Kubo. On the pointwise decay estimate for the wave equation with compactly supported forcing term. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1469-1480. doi: 10.3934/cpaa.2015.14.1469

[15]

L.R. Ritter, Akif Ibragimov, Jay R. Walton, Catherine J. McNeal. Stability analysis using an energy estimate approach of a reaction-diffusion model of atherogenesis. Conference Publications, 2009, 2009 (Special) : 630-639. doi: 10.3934/proc.2009.2009.630

[16]

Zhi-Min Chen. Straightforward approximation of the translating and pulsating free surface Green function. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2767-2783. doi: 10.3934/dcdsb.2014.19.2767

[17]

Claudia Bucur. Some observations on the Green function for the ball in the fractional Laplace framework. Communications on Pure & Applied Analysis, 2016, 15 (2) : 657-699. doi: 10.3934/cpaa.2016.15.657

[18]

Aymen Jbalia. On a logarithmic stability estimate for an inverse heat conduction problem. Mathematical Control & Related Fields, 2019, 9 (2) : 277-287. doi: 10.3934/mcrf.2019014

[19]

Katarzyna PichÓr, Ryszard Rudnicki. Stability of stochastic semigroups and applications to Stein's neuronal model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 377-385. doi: 10.3934/dcdsb.2018026

[20]

Pavel Krejčí, Songmu Zheng. Pointwise asymptotic convergence of solutions for a phase separation model. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 1-18. doi: 10.3934/dcds.2006.16.1

2018 Impact Factor: 0.871

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]