Journal article
Critical thresholds in hyperbolic relaxation systems
Journal of Differential Equations, Vol.247(1), pp.33-48
2009
DOI: 10.1016/j.jde.2009.03.032
Abstract
Critical threshold phenomena in one-dimensional
2
×
2
quasi-linear hyperbolic relaxation systems are investigated. Assuming both the subcharacteristic condition and genuine nonlinearity of the flux, we prove global in time regularity and finite-time singularity formation of solutions simultaneously by showing the critical threshold phenomena associated with the underlying relaxation systems. Our results apply to the well-known isentropic Euler system with damping. Within the same framework it is also shown that the solution of the semi-linear relaxation system remains smooth for all time, provided the subcharacteristic condition is satisfied.
Details
- Title: Subtitle
- Critical thresholds in hyperbolic relaxation systems
- Creators
- Tong Li - University of IowaHailiang Liu - Iowa State University
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.247(1), pp.33-48
- DOI
- 10.1016/j.jde.2009.03.032
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984241040802771
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