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-plas tic SCM model is considered. The gradient operator of the plastic deformati on power rate functional is deduced. it is strictly monotone mapping. Furth er, it is proved that the frictional power rate functional is a convex func tional and the tensional stress power rate functional is a linear one. Henc e, the total power rate functional is a strictly convex functional. By usin g nonlinear functional analysis methods, the existence and uniqueness of ex treme point of the functional is obtained.