  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-Friederichs scheme.
