Evolutionary model of the plane plastic flow of a material with allowance for inertial forces

We consider a system of four quasi-linear first-order differential equations describing the planar plastic flow of a material outside of a convex hole taking into account the effect of inertia. It is shown that the system has two sets of multiple real characteristics, for each one eigenvector and one adjoined vector are appropriate. For this reason, this model is not hyperbolic in the classical sense. The system of equations is transformed into a set of evolutionary equations, which is used for numerical calculations illustrating the effect of inertia forces on the main parameters of the flow