Journal article
THE GENERALIZED RIEMANN PROBLEM AND INSTABILITY OF DELTA SHOCK TO THE CHROMATOGRAPHY EQUATIONS
Communications in mathematical sciences, Vol.16(3), pp.705-734
01/01/2018
DOI: 10.4310/CMS.2018.v16.n3.a5
Abstract
The generalized Riemann problem for the nonlinear chromatography equations in a neighborhood of the origin (t > 0) on the (x, t) plane is considered. The problem is quite different from the previous generalized Riemann problems which have no delta shock wave in the corresponding Riemann solutions. With the method of characteristic analysis and the local existence and uniqueness theorem proposed by Li Ta-tsien and Yu Wen-ci [T.T. Li and W.C. Yu, Univ. Math. Ser. V, Durham, NC, 1985], we constructively solve the generalized Riemann problem and prove the existence and uniqueness of the solutions. It is proved that the generalized Riemann solutions possess a structure similar to the solution of the corresponding Riemann problem for most cases. In case that there is a delta shock wave in the corresponding Riemann solution, we discover that the generalized Riemann solution may turn into a combination of a shock wave and a contact discontinuity, which shows the instability and the internal mechanisms of a delta shock wave.
Details
- Title: Subtitle
- THE GENERALIZED RIEMANN PROBLEM AND INSTABILITY OF DELTA SHOCK TO THE CHROMATOGRAPHY EQUATIONS
- Creators
- Lijun Pan - Nanjing University of Aeronautics and AstronauticsXinli Han - Nanjing University of Posts and TelecommunicationsTong Li - University of IowaLihui Guo - Xinjiang University
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical sciences, Vol.16(3), pp.705-734
- Publisher
- INT PRESS BOSTON, INC
- DOI
- 10.4310/CMS.2018.v16.n3.a5
- ISSN
- 1539-6746
- eISSN
- 1945-0796
- Number of pages
- 30
- Grant note
- Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidents XJEDU2014I001 / Scientific Research Program of the Higher Education Institution of Xinjiang BK20130779 / NSF of Jiangsu Province of China; Natural Science Foundation of Jiangsu Province China Scholarship Council; China Scholarship Council 2013M531343 / China postdoctoral Science Foundation; China Postdoctoral Science Foundation NZ2014107 / Fundamental Research Funds for the Central Universities; Fundamental Research Funds for the Central Universities 11301264; 11401508 / NSF of China; National Natural Science Foundation of China (NSFC)
- Language
- English
- Date published
- 01/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984242422902771
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