A mathematical model of the motion of shear shock waves of nonzero curvature based on their evolution equation

We study particular features of the appearance and motion of 1-dimensional shear shock waves of nonzero curvature basing on the corresponding evolution equation. Using numerous examples of boundary value problems for axisymmetric antiplane deformation, we demonstrate the efficiency of applying solutions to the evolution equation as the frontal asymptotics in the method of matched asymptotic expansions.