针对刚塑性可压缩材料模型热轧过程的总能耗率泛函极值的存在与唯一性问题 ,求出了塑性变形功率泛函的梯度映射 ,它是严格单调的 .进一步地 ,证明了表面摩擦功率泛函是连续凸泛函以及外力功率泛函是线性有界泛函 .因而关于位移速度的总能耗率泛函是严格凸的 .利用非线性泛函分析的方法得到了该泛函的极值点存在且唯一 . In view of the existence and uniqueness of the extremum of the total energy dissipation rate function for the hot-rolling process of a rigid plastic compressible material model, a graded mapping of plastic deformation power functional is obtained, which is strictly monotonous.Furthermore, Frictional power functional is a continuous convex functional and the external power functional is a linear bounded function, so the total energy dissipation rate functional about the displacement velocity is strictly convex. The functional is obtained by nonlinear functional analysis The extremum points exist and are unique.