An analysis of a 2 × 2 Keyfitz–Kranzer type balance system with varying generalized Chaplygin gas.

We consider a system of two balance laws of Keyfitz–Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and the inverse of a power of the density. The Chaplygin gas is a fluid designed to accommodate measurements for the early universe and late-time universal expansion while obeying the pressure–density–time relation. We produce an explanation and description of the non-self-similar Riemann solutions, including the non-classical singular solutions. We also find that due to a direct dependence on time, a change in the regions allowing for combinations of classical and non-classical singular solutions occurs; therefore, a Riemann solution can have different solutions over several time intervals. Our findings are confirmed numerically using the Local Lax–Friedrichs scheme. [ABSTRACT FROM AUTHOR]