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Exact solutions and conservation laws of a one-dimensional PDE model for a blood vessel

Author

Listed:
  • Anco, Stephen C.
  • Garrido, Tamara M.
  • Márquez, Almudena P.
  • Gandarias, María L.

Abstract

Two aspects of a widely used 1D model of blood flow in a single blood vessel are studied by symmetry analysis, where the variables in the model are the blood pressure and the cross-section area of the blood vessel. As one main result, all travelling wave solutions are found by explicit quadrature of the model. The features, behaviour, and boundary conditions for these solutions are discussed. Solutions of interest include shock waves and sharp wave-front pulses for the pressure and the blood flow. Another main result is that three new conservation laws are derived for inviscid flows. Compared to the well-known conservation laws in 1D compressible fluid flow, they describe generalized momentum and generalized axial and volumetric energies. For viscous flows, these conservation laws get replaced by conservation balance equations which contain a dissipative term proportional to the friction coefficient in the model.

Suggested Citation

  • Anco, Stephen C. & Garrido, Tamara M. & Márquez, Almudena P. & Gandarias, María L., 2023. "Exact solutions and conservation laws of a one-dimensional PDE model for a blood vessel," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002618
    DOI: 10.1016/j.chaos.2023.113360
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    References listed on IDEAS

    as
    1. Spiller, C. & Toro, E.F. & Vázquez-Cendón, M.E. & Contarino, C., 2017. "On the exact solution of the Riemann problem for blood flow in human veins, including collapse," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 178-189.
    2. Krivovichev, Gerasim V., 2022. "Comparison of inviscid and viscid one-dimensional models of blood flow in arteries," Applied Mathematics and Computation, Elsevier, vol. 418(C).
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    2. Krivovichev, Gerasim V., 2022. "Comparison of inviscid and viscid one-dimensional models of blood flow in arteries," Applied Mathematics and Computation, Elsevier, vol. 418(C).

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