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Research articles

ScienceAsia 41(2015): 198-204 |doi: 10.2306/scienceasia1513-1874.2015.41.198

The porous medium equation as the relaxation limit of the isentropic Euler equations

Hongli Wanga,*, Huimin Liub

ABSTRACT:     This work is concerned with the relaxation limits of compressible and isentropic Euler equations. For well prepared initial data, the convergence of solution of the compressible Euler equations to the solution of the porous medium equation is justified by an analysis of asymptotic expansions up to any order and a uniform energy estimate.

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a College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450045, Henan Province, China
b General Subjects Department, Zhengzhou Chenggong University of Finance and Economics, Zhengzhou 451200, Henan Province, China

* Corresponding author, E-mail: wanghongli@ncwu.edu.cn

Received 27 Aug 2014, Accepted 26 Apr 2015