On the set of limit values of local diffeomorphisms in wavefront evolution

We study the problem of the appearance of nonsmooth singularities in the evolution of plane wavefronts in the Dirichlet problem for a first-order partial differential equation. The approach to investigating the singularities is based on the properties of local diffeomorphisms. A generalization of the classical notion of a derivative is introduced, which coincides in particular cases with the Schwarz derivative. The results of modeling solutions of nonsmooth dynamic problems are presented.