The Existence of Zero Waves for Nonsimplified Chromatography System

The Existence of Zero Waves for Nonsimplified Chromatography System

In this paper, we mainly consider Riemann problem for the widely used nonsimplified chromatography system with initial data consisting of three pieces of constant states. Through phase plane analysis, the solutions of the nonsimplified chromatography system are established. When the different initia...

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Main Authors: Maozhou Lin, Lihui Guo, Yinsong Bai
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/1970505
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spelling doaj-d3ca9795c76244898aa7b81ac2ebf8312020-11-25T01:25:25ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/19705051970505The Existence of Zero Waves for Nonsimplified Chromatography SystemMaozhou Lin0Lihui Guo1Yinsong Bai2College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaIn this paper, we mainly consider Riemann problem for the widely used nonsimplified chromatography system with initial data consisting of three pieces of constant states. Through phase plane analysis, the solutions of the nonsimplified chromatography system are established. When the different initial data tend to −1 from the right side, the existence of zero shock wave, zero delta shock wave, and zero rarefaction wave is obtained via analyzing its wave interaction. Finally, the correctness of the main conclusions is verified by numerical simulation, and the numerical results are in good agreement with the theoretical solutions of several experimental cases.http://dx.doi.org/10.1155/2020/1970505
collection DOAJ
language English
format Article
sources DOAJ
author Maozhou Lin
Lihui Guo
Yinsong Bai
spellingShingle Maozhou Lin
Lihui Guo
Yinsong Bai
The Existence of Zero Waves for Nonsimplified Chromatography System
Mathematical Problems in Engineering
author_facet Maozhou Lin
Lihui Guo
Yinsong Bai
author_sort Maozhou Lin
title The Existence of Zero Waves for Nonsimplified Chromatography System
title_short The Existence of Zero Waves for Nonsimplified Chromatography System
title_full The Existence of Zero Waves for Nonsimplified Chromatography System
title_fullStr The Existence of Zero Waves for Nonsimplified Chromatography System
title_full_unstemmed The Existence of Zero Waves for Nonsimplified Chromatography System
title_sort existence of zero waves for nonsimplified chromatography system
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description In this paper, we mainly consider Riemann problem for the widely used nonsimplified chromatography system with initial data consisting of three pieces of constant states. Through phase plane analysis, the solutions of the nonsimplified chromatography system are established. When the different initial data tend to −1 from the right side, the existence of zero shock wave, zero delta shock wave, and zero rarefaction wave is obtained via analyzing its wave interaction. Finally, the correctness of the main conclusions is verified by numerical simulation, and the numerical results are in good agreement with the theoretical solutions of several experimental cases.
url http://dx.doi.org/10.1155/2020/1970505
work_keys_str_mv AT maozhoulin theexistenceofzerowavesfornonsimplifiedchromatographysystem
AT lihuiguo theexistenceofzerowavesfornonsimplifiedchromatographysystem
AT yinsongbai theexistenceofzerowavesfornonsimplifiedchromatographysystem
AT maozhoulin existenceofzerowavesfornonsimplifiedchromatographysystem
AT lihuiguo existenceofzerowavesfornonsimplifiedchromatographysystem
AT yinsongbai existenceofzerowavesfornonsimplifiedchromatographysystem
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