Journal article
CRITICAL THRESHOLDS IN A QUASILINEAR HYPERBOLIC MODEL OF BLOOD FLOW
Networks and heterogeneous media, Vol.4(3), pp.527-536
09/01/2009
DOI: 10.3934/nhm.2009.4.527
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.
Details
- Title: Subtitle
- CRITICAL THRESHOLDS IN A QUASILINEAR HYPERBOLIC MODEL OF BLOOD FLOW
- Creators
- Tong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USASuncica Canic - Univ Houston, Dept Math, Houston, TX 77204 USA
- Resource Type
- Journal article
- Publication Details
- Networks and heterogeneous media, Vol.4(3), pp.527-536
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- DOI
- 10.3934/nhm.2009.4.527
- ISSN
- 1556-1801
- eISSN
- 1556-181X
- Number of pages
- 10
- Grant note
- DMS-0806941 / NSF DMS-0443826 / NIH/NIGMS
- Language
- English
- Date published
- 09/01/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984241041702771
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