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A Limiting Viscosity Approach to the Riemann Problem in Blood Flow Through Artery

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Abstract

In this article, we consider the Riemann problem with arbitrary initial data for one-dimensional blood flow equations in the arterial circulation. Here, we establish the existence of the self-similar solution to the Riemann problem by limiting viscosity approach. We convert the Riemann problem to a boundary value problem by adding a suitable viscosity term and establish the existence of the solution. Finally, we construct the existence of the solution to this Riemann problem in the presence of vacuum state.

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Author notes

  1. Rakib Mondal and Minhajul have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science Pilani, K. K. Birla Goa Campus, Sancoale, Goa, 403726, India

    Rakib Mondal &  Minhajul

Authors
  1. Rakib Mondal
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  2. Minhajul
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Correspondence to Minhajul.

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Communicated by Rosihan M. Ali.

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Mondal, R., Minhajul A Limiting Viscosity Approach to the Riemann Problem in Blood Flow Through Artery. Bull. Malays. Math. Sci. Soc. 46, 184 (2023). https://doi.org/10.1007/s40840-023-01579-y

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  • DOI: https://doi.org/10.1007/s40840-023-01579-y

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