Global stability of rarefaction wave to the 1-D piston problem for the Compressible Full Euler Equations

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• 作者：Min Ding^a ; ^{minding12@whut.edu.cn} ; ^{minding12@gmail.com} ; Jie Kuang^b ; ^c ; ^{jkuang@amss.ac.cn} ; ^{jkuang12@fudan.edu.cn} ; Yongqian Zhang^c ; ^{yongqianz@fudan.edu.cn}
• 关键词：Piston problem ; Compressible Euler equations ; Rarefaction wave ; Wave front tracking method ; Interaction of waves ; Asymptotic behavior
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1228-1264
• 全文大小：602 K
• 卷排序：448

文摘

In this paper, we study the 1-D piston problem for compressible full Euler equations under the assumptions that the total variation of the initial data and the perturbation of the piston velocity are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Moreover, we establish the asymptotic behavior of the solutions as t→∞t→∞.