Riemann problems for the 2-D pressureless gas dynamics with external forces

This paper is concerned with the pressureless gas dynamics with a space-dependent gravity or a time-dependent friction in two dimensions. The basic Riemann problems with two pieces of constant initial data are considered. By the characteristic analysis, the Riemann problems are constructively solved by two kinds of solutions: vacuum solution and delta-shock solution, which describe the phenomena of cavitation and concentration, respectively. Especially, the generalized Rankine-Hugoniot relations for delta-shock waves are clarified and applied to the Riemann problems.