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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
Tong Li 1, and Kun Zhao 2,
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419
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.
Keywords: Large data, Large-time behavior., Initial-boundary value problem, Blood flow, Entropy weak solution, Hyperbolic balance laws, Global existence.
Mathematics Subject Classification: Primary: 35L50, 35L65; Secondary: 92C3.
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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Tong Li Kun Zhao