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Critical thresholds in hyperbolic relaxation systems
Journal article   Open access   Peer reviewed

Critical thresholds in hyperbolic relaxation systems

Tong Li and Hailiang Liu
Journal of Differential Equations, Vol.247(1), pp.33-48
2009
DOI: 10.1016/j.jde.2009.03.032
url
https://doi.org/10.1016/j.jde.2009.03.032View
Published (Version of record) Open Access

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.
Critical thresholds Finite-time singularity Global regularity Quasi-linear relaxation model

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