Interactions of Elementary Waves for the Nonlinear Chromatography Equations

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• 作者：Xiaoxia Wang ; Lihui Guo ; Gan Yin
• 关键词：Elementary waves ; Interaction ; Linear degenerate ; Chromatography equations ; Riemann problem ; 35L65 ; 35L67 ; 76L05 ; 76N10
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：39
• 期：1
• 页码：391-407
• 全文大小：831 KB
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• 作者单位：Xiaoxia Wang (1)
  Lihui Guo (1)
  Gan Yin (1)
  
  1. College of Mathematics and System Sciences, Xinjiang University, Ürümqi, 830046, People’s Republic of China
  
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206

文摘

In this article, we study the global solution of the elementary waves interaction problem for the nonlinear chromatography equations. We constructively obtain the solutions when the initial data are three piecewise constant states. The global structures and large time-asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, it is easy to see that the solutions of the perturbed Riemann problem converge to nothing but the corresponding Riemann solutions as \(\epsilon \rightarrow 0\), from which the stability of the Riemann solutions with respect to this local small perturbation of the Riemann initial data are obtained. Keywords Elementary waves Interaction Linear degenerate Chromatography equations Riemann problem