| Formation and Transition of Delta Shock in the Limits of Riemann Solutions to the Perturbed Chromatography Equations |
| Received:January 23, 2018 Revised:July 17, 2018 |
| Key Words:
chromatography equations perturbation delta shock formation transition
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11301264), China Scholarship Council, China Postdoctoral Science Foundation (Grant No.2013M531343), the Fundamental Research Funds for the Central Universities (Grant No.NZ2014107), Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-Aged Teachers and Presidents, the Natural Science of Jiangsu Province (Grant No.BK20130779). |
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| Abstract: |
| This paper is concerned with the formation and transition of delta shock solutions to the perturbed chromatography equations. We discuss the Riemann problem for the perturbed chromatography equations. By studying the limits of the Riemann solutions as the perturbation parameter tends to zero, we can observe two important phenomena. One is that a shock and a contact discontinuity coincide to form a delta shock. The second is that the transition from one kind of delta shock on which two state variables simultaneously contain the Dirac delta function, to another kind of delta shock on which only one state variable contains the Dirac delta function. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.01.007 |
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