Overcompressive shocks in a 2×2 hyperbolic system of conservation laws
A. P. Chugainova, R. R. Polekhina, D. V. Treschev
Abstract
Overcompressive shocks in a 2×2 hyperbolic system of conservation laws describing small-amplitude longitudinal-torsional waves in an elastic rod are investigated. A viscous regularization method with an anisotropic dissipative matrix is applied to the system. A qualitative analysis of phase portraits has revealed that a two-parameter family of heteroclinic trajectories, representing the structure of an overcompressive shock, exists in one of six domains in the parameter plane. It is established that the model admits overcompressive shocks, which belong to the first type according to the classification of Liu.
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