Tong Li (Department of Mathematics, University of Iowa)
(October 23, 2008 10:30 AM - 11:30 AM)
Critical threshold phenomena in a one dimensional quasi-linear hyperbolic model of blood flow is investigated. We prove global in time regularity and finite time singularity formation of solutions simultaneously by showing the critical threshold phenomena associated with the underlying model of blood flow.
We obtain that for the certain form of the pressure data one can guarantee smooth solution, but for the physiologically relevant data one has shock formation. This is a joint work with Suncica Canic.