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March  2006, 1(1): 167-183. doi: 10.3934/nhm.2006.1.167

The Green's functions for the Broadwell Model in a half space problem

Chiu-Ya Lan 1, , Huey-Er Lin 2, and  Shih-Hsien Yu 3,

1. 

Department of Applied Mathematics, National Sun Yet-sen University, Kaohsiung, Taiwan
2. 

Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan
3. 

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

Received  September 2005 Revised  November 2005 Published  January 2006

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 $L^2$-boundary data into $L^\infty$ 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.
Keywords: initial-boundary value problem., Broadwell model.
Mathematics Subject Classification: Primary: 82C4.
Citation: 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
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