arXiv subjects

A. P. Chugainova

Publications and source records attributed to A. P. Chugainova.

2 recordsLinked to original sources

arXiv2026

Overcompressive shocks in a $2\times2$ hyperbolic system of conservation laws

Overcompressive shocks in a $2\times2$ 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.

math-ph↗

arXiv2025

Waves, structures, and the Riemann problem for a system of hyperbolic conservation laws

A system of hyperbolic conservation laws $$ \partial_t u + \partial_x \partial_u Q = 0, \quad Q = u_1^3 / 3 + u_1 u_2^2, \qquad u = u(x,t) \in\mR^2, $$ as well as its viscous regularization $$ \partial_t u + \partial_x \partial_u Q = \calM \partial_x^2 u, \qquad \calM = \diag (μ_1,μ_2), \quad μ_1>0,\, μ_2>0, $$ are studied. It is assumed that admissible shocks are those that satisfy the requirement of existence of a structure (the traveling wave criterion). A solution of the Riemann problem is constructed that consists of rarefaction waves and shocks with structure. Depending on the conditions imposed at $\pm\infty$, the solution also contains undercompressive shocks and Jouguet waves.

math-ph↗