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Global Solutions of the Perturbed Riemann Problem for the Chromatography Equations

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Abstract

The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann problem. In addition, it can be observed that the Riemann solutions are stable under small perturbations of the Riemann initial data.

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Acknowledgements

The frist author would like to express her gratitude to all those who helped her during the writing of this thesis.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Shanghai University, Shanghai, 200444, China

    Ting Zhang  (张婷) & Wancheng Sheng  (盛万成)

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  1. Ting Zhang  (张婷)
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  2. Wancheng Sheng  (盛万成)
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Corresponding author

Correspondence to Wancheng Sheng  (盛万成).

Additional information

Supported by NSFC (11371240 and 11771274), and the grant of “The First-Class Discipline of Universities in Shanghai”.

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Zhang, T., Sheng, W. Global Solutions of the Perturbed Riemann Problem for the Chromatography Equations. Acta Math Sci 39, 57–82 (2019). https://doi.org/10.1007/s10473-019-0106-9

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  • DOI: https://doi.org/10.1007/s10473-019-0106-9

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