Generalized Plane Delta-Shock Waves for n-Dimensional Zero-Pressure Gas Dynamics

With the help of a generalized plane wave solution, we study a type of generalized plane delta-shock wave for the n-dimensional zero-pressure gas dynamics and refine its generalized Rankine–Hugoniot relation which is a system of ordinary equations. This relation describes accurately the character of the generalized plane delta-shock: location, propagation speed, and weight. Under a suitable entropy condition, four different explicit constructions of solutions for a kind of Riemann problem with Radon measure as initial data are established uniquely. The overtaking of two plane delta-shocks forming a new generalized plane delta-shock is also investigated. Finally, the 2-D Riemann problem with four pieces of initial data is solved in a simplified situation.