一类微分半变分不等式问题研究

In 2008, Pang and Stewart introduced and studied a class of differential variational inequalities in finite-dimensional spaces. The research has important theoretical value and application prospect. many researchers at home and abroad have made achievements in studying the theory, algorithm and applications of differential variational inequality in recent years. This project will study the theory and algorithm of a class of differential hemivariational inequalities. We will establish sufficient conditions for the existence of the solution of differential hemivariational inequalities by using nonlinear analysis, differential equation and optimization theory and methods. Then we establish an algorithm for the problem and show the analysis of convergence in a similar way to Euler time-stepping procedure and Tikhonov regularized time-stepping methods for differential variational inequalities. The results of this project not only enrich and develop the theory and algorithm of differential variational inequalities, but also has broad prospect of application in mechanics and engineering.

2008年，Pang和Stewart在有限维空间中引入并研究了一类微分变分不等式，这项研究具有重要的理论意义和应用前景。近年来，国内外有不少学者对一些微分变分不等式的理论、算法及应用进行了研究，获得了许多有价值的研究成果。本项目主要研究一类微分半变分不等式的理论和算法。利用非线性分析、微分方程和优化理论的方法和技巧，获得这类问题解存在的充分性条件。借鉴研究微分变分不等式的欧拉时步进程和Tikhonov正则时步算法，构造这类微分半变分不等式解的逼近算法，分析算法的收敛性。本项目的研究，不仅可以丰富和发展微分变分不等式的相关理论与算法，而且在力学、工程学等领域具有广泛的应用前景。

本项目的主要目的是引入并研究一类微分半变分不等式问题。利用非线性分析、微分方程和优化理论的方法和技巧，获得这类问题解存在的充分性条件。借鉴微分变分不等式已有的欧拉时步进程和Tikhonov正则时步算法，构造这类微分半变分不等式解的逼近算法，分析算法的收敛性。