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

Tong Li; Kun Zhao

doi:10.3934/nhm.2011.6.625

Article Contents

2011, Volume 6, Issue 4: 625-646. Doi: 10.3934/nhm.2011.6.625

This issue Previous Article Multiscale model of tumor-derived capillary-like network formation Next Article A model for biological dynamic networks

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

Tong Li^1, and
Kun Zhao^2,

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

Received: March 31, 2010

Revised: April 30, 2011

Published: November 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L50, 35L65; Secondary: 92C35.

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