Best asymptotic profile for the system of compressible adiabatic flow through porous media on quadrant

Shifeng Geng; Zhen Wang

doi:10.3934/cpaa.2012.11.475

Article Contents

2012, Volume 11, Issue 2: 475-500. Doi: 10.3934/cpaa.2012.11.475

This issue Previous Article Lyapunov-type inequalities for even order differential equations Next Article The estimate of the multi-scale homogenization method for Green's function on Sobolev space $W^{1,q}(\Omega)$

Best asymptotic profile for the system of compressible adiabatic flow through porous media on quadrant

Shifeng Geng^1, and
Zhen Wang^2,

1.
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105
2.
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071

Received: July 31, 2010

Revised: December 31, 2010

Published: February 2012

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Abstract

We realize the best asymptotic profile for the solutions to the nonisentropic $p$-system with damping on quadrant is a particular solution of the IBVP for the corresponding nonlinear parabolic equation with special initial data, and we further show the convergence rates to this particular asymptotic profile. This rates are same to that for the isentropic case obtained by H. Ma and M. Mei (J. Differential Equations 249 (2010), 446--484).

Keywords:

Asymptotic behavior,
the system of compressible adiabatic flow,
boundary effect,
convergence rates.

Mathematics Subject Classification: 35B40, 35L50, 35L65, 76R50.

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References

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