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Overcompressive shocks in a 2×2 hyperbolic system of conservation laws
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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BibTeX
@misc{chugainova2026overcompressive,
title = {{Overcompressive shocks in a $2\times2$ hyperbolic system of conservation laws}},
author = {A. P. Chugainova and R. R. Polekhina and D. V. Treschev},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08292},
eprint = {2611.08292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08292},
}
RIS
TY - UNPB
TI - Overcompressive shocks in a 2×2 hyperbolic system of conservation laws
AU - A. P. Chugainova
AU - R. R. Polekhina
AU - D. V. Treschev
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08292
UR - https://arxiv.org/abs/2611.08292
AB - 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.
ER -