Bulletin of the
Korean Mathematical Society BKMS

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including delta-shock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the limiting viscosity method.

Keywords: Pressureless Euler system; Source term; Non-self-similar solutions; Delta-shock; Limiting viscosity method.

MSC numbers: 35L65,35L67,35B30