Exact Solutions to an Evolution Equation of Plastic Layer Flow on a Plane / V. A. Kadymov, E. N. Sosenushkin, and E. A. Yanovskaya. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 3. P. 61-66 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 69-72].
The flow of a thin plastic layer between two rigid plates approaching each other in the normal direction is considered. The kinematics of plastic layer flow is studied. An evolution equation describing the free boundary of the flow region is derived. The similarity solutions to this equation are analyzed. It is shown that the evolution equation can be reduced to a particular case of the nonlinear heat conduction equation. New exact particular solutions to the evolution equation are obtained using the variable separation method and the method of self-similar transformations.
Key words: plastic layer compression, boundary value problem formulation, free flow on the plane, boundary evolution equation.