Existence and uniqueness of extreme point of total power rate functional for hot rolling problem with rigid-plastic SCM model

The total power rate functional for hot rolling problem with the rigid-plastic SCM model is considered. The gradient operator of the plastic deformation power rate functional is deduced. It is strictly monotone mapping. Further, it is proved that the frictional power rate functional is a convex functional and the tensional stress power rate functional is a linear one. Hence, the total power rate functional is a strictly convex functional. By using nonlinear functional analysis methods, the existence and uniqueness of extreme point of the functional is obtained.