ABSTRACT
One of the most interesting applications of the theory of generalized functions is the problem of propagation and interaction of singularities. Nonsmooth solutions of nonlinear equations are very important from the physical viewpoint, since they describe such actual phenomena as shock waves, typhoons, tsunami waves, and so on. This chapter discusses the approach related to Maslov’s ideas and the process of shock wave propagation. It is well-known that to solve a linear problem of determining the trajectory of a singularity, it suffices to construct an approximating solution that satisfies the equation up to a sufficiently smooth function. The chapter presents the Maslov scheme for calculating the shock wave propagation, using only ordinary differential equations.
