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On the Existence of Global Weak Solutions to 1D Pollutant Transport Model

Author

Listed:
  • Brahima ROAMBA
  • Jean de Dieu ZABSONRE
  • Yacouba ZONGO

Abstract

We consider a one-dimensionnal bilayer model coupling shallow water and Reynolds lubrication equations with a molecular interactions between molecules. These molecular interactions give rise to intermolecular forces, namely the long-range van der Waals forces and short-range Born intermolecular forces. In this paper, an expression will be used to take into account all these intermolecular forces. Our model is a similar model studied in (Roamba, Zabsonr\'{e}\& Zongo, 2017). The model considered is represented by the two superposed immiscible fluids. A similar model was studied in (Zabsonr\'{e} Lucas \& Fernandez-Nieto, 2009) but the authors do not take into account the intermolecular forces. Without hypothesis about the unknowns as in (Roamba, Zabsonr\'{e}\& Zongo, 2017), we show the existence of global weak solution in time in a periodic domain.

Suggested Citation

  • Brahima ROAMBA & Jean de Dieu ZABSONRE & Yacouba ZONGO, 2017. "On the Existence of Global Weak Solutions to 1D Pollutant Transport Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 124-134, August.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:124-134
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    Citations

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    Cited by:

    1. Brahima ROAMBA, 2021. "Another Proof of Existence of Global Weak Solutions to 1D Pollutant Transport Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(2), pages 1-31, April.
    2. Yacouba ZONGO & Brahima ROAMBA & Boulaye YIRA, 2020. "On the Construction of Approximate Solutions for the 1D Pollutant Transport Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(3), pages 1-1, June.

    More about this item

    Keywords

    shallow water equations; bilayer models; viscosity; friction; capillarity; intermolecular forces;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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