# American Institute of Mathematical Sciences

March  2019, 8(1): 221-230. doi: 10.3934/eect.2019012

## Shock wave formation in compliant arteries

 1 Division of Imaging Sciences and Biomedical Engineering, King's College London, St. Thomas' Hospital, SE1 7EH London, United Kingdom 2 Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, E-46022 València, Spain 3 CoMMLab, Departament d'Informàtica, Universitat de València, E-46100 Burjassot, València, Spain

* Corresponding author: J. Alberto Conejero

Received  March 2018 Revised  July 2018 Published  March 2019 Early access  January 2019

We focus on the problem of shock wave formation in a model of blood flow along an elastic artery. We analyze the conditions under which this phenomenon can appear and we provide an estimation of the instant of shock formation. Numerical simulations of the model have been conducted using the Discontinuous Galerkin Finite Element Method. The results are consistent with certain phenomena observed by practitioners in patients with arteriopathies, and they could predict the possible formation of a shock wave in the aorta.

Citation: Cristóbal Rodero, J. Alberto Conejero, Ignacio García-Fernández. Shock wave formation in compliant arteries. Evolution Equations & Control Theory, 2019, 8 (1) : 221-230. doi: 10.3934/eect.2019012
##### References:

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##### References:
An artery as a compliant tube, where variable x denotes the spatial coordinate and t the temporal one.
Decomposition of the domain $D$.
Several beat like boundary conditions (23) for $u(0, 0) = 0$.
Formation of a shock wave with a beat-like boundary condition. The discontinuity at $x = 20$ is due to the nature of the DG method, which provides two values in the frontier between elements.
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