This paper focuses on the isentropic Euler system for the Born-Infeld equation of state with friction, for which the Riemann problem is solved by applying the variable substitution method. The non-self-similar Riemann solutions with five different structures are obtained. Although the considered system with non-negative pressure is strictly hyperbolic with two genuinely nonlinear characteristic fields, the delta shock wave still occurs in the solutions. For the delta shock wave, the generalized Rankine-Hugoniot relation and entropy condition are clarified. Under the impact of the friction term, the rarefaction waves and shock waves as well as delta shock wave are bent into parabolic curves. Also, it is shown that as the pressure goes to zero, the non-self-similar solutions of the considered system just converge to the non-self-similar solutions of the zero-pressure Euler system with friction.
Li et al. (Mon,) studied this question.