Asymptotic behavior of solutions to a model system of a radiating gas

Yongqin Liu; Shuichi Kawashima

doi:10.3934/cpaa.2011.10.209

Article Contents

2011, Volume 10, Issue 1: 209-223. Doi: 10.3934/cpaa.2011.10.209

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Asymptotic behavior of solutions to a model system of a radiating gas

Yongqin Liu^1, and
Shuichi Kawashima^1,

1.
Faculty of Mathematics, Kyushu University, Fukuoka 819-0395

Received: December 31, 2009

Revised: March 31, 2010

Published: December 2010

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Abstract

In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates of solutions. Moreover, we show that the solution is asymptotic to the linear diffusion wave which is given in terms of the heat kernel.

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Mathematics Subject Classification: 35B40, 35M20.

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