Critical thresholds in a quasilinear hyperbolic model of blood flow

Tong Li; Sunčica Čanić

doi:10.3934/nhm.2009.4.527

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2009, Volume 4, Issue 3: 527-536. Doi: 10.3934/nhm.2009.4.527

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Critical thresholds in a quasilinear hyperbolic model of blood flow

Tong Li^1, and
Sunčica Čanić^2,

1.
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419
2.
Department of Mathematics, University of Houston, Houston, TX 77204-3476

Received: October 31, 2008

Revised: April 30, 2009

Published: August 2009

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Abstract

Critical threshold phenomena in a one dimensional quasi-linear hyperbolic model of blood flow with viscous damping are investigated. We prove global in time regularity and finite time singularity formation of solutions simultaneously by showing the critical threshold phenomena associated with the blood flow model. New results are obtained showing that the class of data that leads to global smooth solutions includes the data with negative initial Riemann invariant slopes and that the magnitude of the negative slope is not necessarily small, but it is determined by the magnitude of the viscous damping. For the data that leads to shock formation, we show that shock formation is delayed due to viscous damping.

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Mathematics Subject Classification: Primary: 35L60, 35L67; Secondary: 35L45, 76L05.

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