This report consists of two parts. In the first part, we introduce the Yosida-regularization system for solving generalized equations of maximum monotone operators in the finite dimensional Hilbert spaces and the Yosida-regularization based acceleration system in infinite dimensional Hilbert spaces. We obtain the convergence rates of differential equation solutions for both systems and the uniform convergence results of the discrete solutions on interval [0,+∞). In the second part, we provide the existence of the gradient flow for the inner optimal value function of the minimax problem under the non-gradient Lipschitz condition of the objective function, as well as a line-searching method derived from the gradient flow.