# American Institute of Mathematical Sciences

December  2011, 6(4): 625-646. doi: 10.3934/nhm.2011.6.625

## Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model

 1 Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419 2 Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States

Received  April 2010 Revised  May 2011 Published  December 2011

This paper is concerned with 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 $L^\infty$ entropy weak solutions exist globally in time when the initial data are large, rough and contains vacuum states. Furthermore, based on entropy principle and the theory of divergence measure field, it is shown that any $L^\infty$ entropy weak solution converges to a constant equilibrium state exponentially fast as time goes to infinity. The physiological relevance of the theoretical results obtained in this paper is demonstrated.
Citation: Tong Li, Kun Zhao. Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model. Networks & Heterogeneous Media, 2011, 6 (4) : 625-646. doi: 10.3934/nhm.2011.6.625
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