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 Word: chromatography equations   perturbation   delta shock   formation   transition  
Fund ProjectL: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).
Author NameAffiliation
Xinlin HAN School of Science, Nanjing University of Posts and Telecommunications, Jiangsu 210023, P. R. China 
Lijun PAN Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Jiangsu 211106, P. R. China 
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      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.
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