Delta shock wave and wave interactions in a hyperbolic system of conservation laws

Abstract  :   In this talk, we discuss the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equations of state with the Coulomb-like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero-pressure gas dynamics system with a body force when the pressure vanishes if we neglect virtual velocity in vacuum region. Later, we study the interaction of delta shock waves for the one-dimensional strictly hyperbolic system of conservation laws. We discuss the stability of the Riemann solution under local small perturbations of the Riemann initial data. The global structure and large time asymptotic behaviour of the perturbed Riemann solutions are constructed and analyzed case by case.