July  2011, 16(1): 333-344. doi: 10.3934/dcdsb.2011.16.333

On a quasilinear hyperbolic system in blood flow modeling

1. 

Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States

2. 

Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States

Received  April 2010 Revised  September 2010 Published  April 2011

This paper aims at an initial-boundary value problem on bounded domains for a one-dimensional quasilinear hyperbolic model of blood flow with viscous damping. It is shown that, for given smooth initial data close to a constant equilibrium state, there exists a unique global smooth solution to the model. Time asymptotically, it is shown that the solution converges to the constant equilibrium state exponentially fast as time goes to infinity due to viscous damping and boundary effects.
Citation: Tong Li, Kun Zhao. On a quasilinear hyperbolic system in blood flow modeling. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 333-344. doi: 10.3934/dcdsb.2011.16.333
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show all references

References:
[1]

Z. Angew. Math. Phys., 22 (1971), 217-246. doi: 10.1007/BF01591407.  Google Scholar

[2]

Biophysical J., 6 (1966), 717-724. doi: 10.1016/S0006-3495(66)86690-0.  Google Scholar

[3]

Comput. Visual. Sci., 4 (2002), 147-155. doi: 10.1126/science.4.83.147.  Google Scholar

[4]

Math. Methods Appl. Sci., 26 (2003), 1161-1186. doi: 10.1002/mma.407.  Google Scholar

[5]

Multiscale Model. Simul., 5 (2005), 559-596.  Google Scholar

[6]

in "Hyperbolic Problems: Theory, Numerics, Applications: Eighth International Conference In Magdeburg, 2000," 227-236, International series of numerical mathematics (eds. H. Freist黨ler and G. Warnecke), 141, Birkh鋟ser, Basel, 2001.  Google Scholar

[7]

Z. Angew. Math. Phys., 46 Special Issue (1995), 294-307.  Google Scholar

[8]

in "Mathematical Modelling and Numerical Simulation in Continuum Mechanics," 137-153, Lecture Notes in Computational Science and Engineering, 19 (eds. I. Babuska, P.G. Ciarbet and T. Miyoshi), Springer-Verlag, Berlin, 2002.  Google Scholar

[9]

Comput. Visual. Sci., 2 (1999), 75-83. Google Scholar

[10]

World Scientific, Singapore, 1998. doi: 10.1142/9789812816917.  Google Scholar

[11]

Netw. Heterog. Media, 4 (2009), 527-536. doi: 10.3934/nhm.2009.4.527.  Google Scholar

[12]

Publ. Math. D'Orsay, (1978), 46-53.  Google Scholar

[13]

J. Differential Equations, 131 (1996), 171-188. doi: 10.1006/jdeq.1996.0159.  Google Scholar

[14]

J. Differentail Equations, 156 (1999), 439-458. doi: 10.1006/jdeq.1998.3598.  Google Scholar

[15]

Annals of Biomedical Engineering, 28 (2000), 1281-1299. doi: 10.1114/1.1326031.  Google Scholar

[16]

J. Differential Equations, 246 (2009), 581-596. doi: 10.1016/j.jde.2008.06.007.  Google Scholar

[17]

SIAM J. Appl. Math., 62 (2002), 990-1018. doi: 10.1137/S0036139999355199.  Google Scholar

[18]

Comm. Partial Differential Equations, 28 (2003), 795-816. doi: 10.1081/PDE-120020497.  Google Scholar

[19]

Oxford Science Publications, 2007.  Google Scholar

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