J. Alastruey, A. W. Khir, K. S. Matthys, P. Segers, S. J. Sherwin et al., Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements, J. Biomech, vol.44, issue.12, pp.2250-2258, 2011.

J. Alastruey, K. H. Parker, J. Peiró, and S. J. Sherwin, Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation, Comm. Comp. Phys, vol.4, pp.317-336, 2008.

F. Berntsson, M. Karlsson, V. Kozlov, and S. Nazarov, A one-dimensional model of viscous blood flow in an elastic vessel, Appl. Math. Comp, vol.274, pp.125-132, 2016.

D. Bessems, M. Rutten, and F. Van-de-vosse, A wave propagation model of blood flow in large vessels using an approximate velocity profile function, J. Fluid Mech, vol.580, pp.145-168, 2007.

J. L. Bona, M. Chen, and J. Saut, Boussinesq equations and other systems for smallamplitude long waves in nonlinear dispersive media. I: Derivation and linear theory, J. Nonlinear Sci, vol.12, pp.283-318, 2002.

R. , Variable coefficient KdV equations and waves in elastic tubes, Evolution Equations, pp.57-70, 2003.

R. , A Boussinesq model for pressure and flow velocity waves in arterial segments, Mathematics and Computers in Simulation, vol.82, issue.6, pp.1047-1055, 2012.

K. B. Chandran, S. E. Rittgers, and A. P. Yoganathan, Biofluid mechanics: the human circulation, 2012.

J. Chehab and G. Sadaka, On damping rates of dissipative KdV equations. Discrete Continuous Dyn, Syst. Ser. B, vol.6, pp.1487-1506, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00734292

H. Demiray, Solitary wave in prestressed elastic tubes, Bulletin of Mathematical Biology, vol.58, pp.939-955, 1996.

H. Demiray, Waves in fluid-filled elastic tubes with a stenosis: Variable coefficients KdV equations, J. Comp. Appl. Math, vol.202, pp.328-338, 2007.
DOI : 10.1016/j.cam.2005.10.043
URL : https://doi.org/10.1016/j.cam.2005.10.043

D. Dutykh and F. Dias, Dissipative Boussinesq equations, C. R. Mécanique, vol.335, pp.559-583, 2007.
DOI : 10.1016/j.crme.2007.08.003
URL : https://hal.archives-ouvertes.fr/hal-00137633

H. A. Erbay, S. Erbay, and S. Dost, Wave propagation in fluid filled nonlinear viscoelastic tubes, Acta Mechanica, vol.95, issue.1, pp.87-102, 1992.
DOI : 10.1007/bf01170806

C. A. Figueroa, I. E. Vignon-clementel, K. E. Jansen, T. J. Hughes, and C. A. Taylor, A coupled momentum method for modeling blood flow in three-dimensional deformable arteries, Comput. Methods Appl. Mech. Engrg, vol.195, issue.41, pp.5685-5706, 2006.

L. Formaggia, D. Lamponi, and A. Quarteroni, One-dimensional models for blood flow in arteries, J.Eng. Math, vol.47, issue.3-4, pp.251-276, 2003.

Y. Fung, Biomechanics: Circulation, 1997.
DOI : 10.1097/00024382-199802000-00018

T. J. Hughes and J. Lubliner, On the one-dimensional theory of blood flow in the larger vessels, Mathematical Biosciences, vol.18, issue.1-2, pp.161-170, 1973.

J. Lagrange, Mémoire sur la théorie du mouvement des fluides, Nouv. Mém. Acad, p.1781

V. Milisi? and A. Quarteroni, Analysis of lumped parameter models for blood flow simulations and their relation with 1D models, ESAIM: Math. Model. Num. Anal, vol.38, pp.613-632, 2004.

D. Mitsotakis, D. Dutykh, and L. Qian, Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry, Computers and Mathematics with Applications, vol.75, pp.4022-4047, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01756720

L. O. Müller and E. F. Toro, Well-balanced high-order solver for blood flow in networks of vessels with variable properties, Int. J. Numer. Meth. Biomed. Engng, vol.29, issue.12, pp.1388-1411, 2013.

J. P. Mynard and P. Nithiarasu, A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method, Commun. Numer. Meth. Engng, vol.24, pp.367-417, 2008.

W. Nichols, M. O'rourke, and C. Vlachopoulos, McDonald's blood flow in arteries: theoretical, experimental and clinical principles, 2011.

M. S. Olufsen, C. S. Peskin, W. Y. Kim, E. M. Pedersen, A. Nadim et al., Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions, Annals of Biomedical Engineering, vol.28, issue.11, pp.1281-1299, 2000.

D. H. Peregrine, Long waves on a beach, J. Fluid Mech, vol.27, pp.815-827, 1967.

K. Perktold and G. Rappitsch, Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model, J. Biomechanics, vol.28, issue.7, pp.845-856, 1995.

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system, Handbook of numerical analysis, vol.12, pp.3-127, 2004.

P. Reymond, Y. Bohraus, F. Perren, F. Lazeyras, and N. Stergiopulos, Validation of a patientspecific one-dimensional model of the systemic arterial tree, American journal of physiology. Heart and circulatory physiology, vol.301, issue.3, pp.1173-1182, 2011.

S. J. Sherwin, . Franke, K. Peirò, and . Parker, One-dimensional modelling of a vascular network in space-time variables, J. Eng. Math, vol.47, issue.3-4, pp.217-250, 2003.

N. P. Smith, A. J. Pullan, and P. J. Hunter, An anatomically based model of transient coronary blood flow in the heart, SIAM J. Appl. Math, vol.62, issue.3, pp.990-1018, 2002.

N. Stergiopulos, D. F. Young, and T. R. Rogge, Computer simulation of arterial flow with applications to arterial and aortic stenoses, Journal of Biomechanics, vol.25, issue.12, pp.1477-1488, 1992.

R. J. Tait, T. Bryant-moodie, and J. B. Haddow, Wave propagation in a fluid-filled elastic tube, Acta Mechanica, vol.38, issue.1, pp.71-83, 1981.

C. A. Taylor, T. J. Hughes, and C. K. Zarins, Finite element modeling of blood flow in arteries, Comp. Methods Appl. Mech. Engrg, vol.158, issue.1-2, pp.155-196, 1998.

F. N. Van-de-vosse and N. Stergiopulos, Pulse wave propagation in the arterial tree, Ann. Rev. Fluid Mech, vol.43, issue.1, pp.467-499, 2011.

X. Wang, J. Fullana, and P. Lagrée, Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model, Computer Methods in Biomechanics and Biomedical Engineering, vol.18, issue.15, pp.1704-1725, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00807040

G. B. Whitham, Linear and nonlinear waves, vol.42, 2011.

N. Xiao, J. Alastruey, and C. A. Figueroa, A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models, Int. J. Numer. Meth. Biomed. Engng, vol.30, issue.2, pp.204-231, 2014.

S. Yomosa, Solitary waves in large blood vessels, Journal of the Physical society of Japan, vol.56, issue.2, pp.506-520, 1987.

M. Zagzoule and J. P. Marc-vergnes, A global mathematical model of the cerebral circulation in man, J. Biomechanics, vol.19, issue.12, pp.1015-1022, 1986.

M. Zamir, New Zealand E-mail address: dimitrios.mitsotakis@vuw.ac, The Physics of Pulsatile Flow, vol.55, p.73000, 2000.

F. E. Chambéry,