Concentration and Cavitation in the Riemann Solutions for the Triple-Pressure Euler Equations Involving a Source Term

The exact solutions for the Riemann problem concerning the one-dimensional triple-pressure Euler equations with the Coulomb-type frictional term are displayed in perfectly explicit forms, where both the rarefaction and shock waves are presented in parabolic shapes with equal curvature under the action of the Coulomb-type frictional term. Specifically, the curved delta shock wave is formed by sending the limit of Riemann solution comprised of double shock waves, and the vacuum state is also grown up by taking the limit of Riemann solution comprised of double rarefaction waves when all the three perturbation parameters are dropped to zero, where the remarkable concentration and cavitation phenomena can be closely observed and explored. Besides, the numerical simulations in correspondence are also offered to validate our results.