Converging shock wave in a dusty gas through nonstandard analysis

A problem of propagation of strong plane and converging shock wave is studied in a mixture of a gas and small solid particles. It is assumed that the solid particles are continuously distributed in the gas. Jump conditions for plane and converging shock waves are derived using the nonstandard analysis. It is also assumed that the shock thickness occurs at infinitesimal interval and jump functions are smooth across this interval. The distribution of flow parameters across the shock wave are presented in terms of Heaviside functions and Dirac Delta measures.