The Green's functions for the Broadwell Model in a half space problem
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Department of Applied Mathematics, National Sun Yet-sen University, Kaohsiung
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Department of Mathematics, National Taiwan Normal University, Taipei
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Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong
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Received:
01 September 2005
Revised:
01 November 2005
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Primary: 82C40.
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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 $L^2$-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.
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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Abstract
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.
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