Some exact solutions of the evolutionary equation for spreading of a plastic layer on a plane

The flow of a thin plastic layer between two rigid plates approaching normal to each other is considered. The kinematics of plastic layer spreading is studied. An evolution equation determining the free boundary of the spreading region is derived. The similarity solutions of 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.