Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping

Abstract

Abstract This paper is focused on the Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions.

Keywords

• Conservation laws
• Time-gradually-degenerate damping
• Delta-shocks
• Vanishing viscosity method