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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

Shijin Deng 1, , Weike Wang 1, and  Shih-Hsien Yu 2,

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.
Keywords: the Green's function, pointwise estimate, the Broadwell model, nonlinear stability.
Mathematics Subject Classification: Primary: 82C4.
Citation: 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
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