Flux approximation limits of solutions to the Suliciu relaxation system with one independent parameter

Abstract Aided by flux-approximation limits of solutions to the Suliciu relaxation system with one independent parameter, we identify the phenomena of concentration and cavitation. It turns out that, as flux perturbation decreases to a certain critical value, any Riemann solution containing two shocks and possibly one-contact-discontinuity of the perturbed Suliciu relaxation system converges to its own delta-shock solution. As the parameter goes to zero further, the limiting solution is just the delta-shock solution of the pressureless gas dynamics model; any Riemann solution containing two rarefaction waves and possibly one contact-discontinuity converges to a solution involving vacuum state of the pressureless gas dynamics model. In the end we show some numerical results to exhibit the formation process of delta shock wave and vacuum states as the flux perturbation decreases.