THE RIEMANN PROBLEM FOR PRESSURELESS FLUID-DYNAMICS WITH DISTRIBUTIONSOLUTIONS IN COLOMBEAUS SENSE

The Riemann problem for the equations of pressureless fluid dynamics w as considered. Solutions of this problem were constructed by employing the viscosity vanishing approach. For some initial data, solutions sh owed high singularity around the shock waves. A new mathematical theor y of generalized functions initiated by J.F. Colombeau was applied to dealing with the multiplication of singular distributions. As a byprod uct, the entropy condition was obtained for singular distribution solu tions.