自2008年，J.S. Pang教授和D.E. Stewart教授的开创性工作以来，利用微分变分不等式来刻画冲击力学、经济动力学、动态交通网络等工程问题已受到了广泛关注。为弥补微分变分不等式在研究非光滑对流反应扩散问题的不适用性，本项目将聚焦一类由抛物型变分-H半变分不等式和非线性发展包含所耦合成的微分变分-H半变分不等式，主要研究内容包括：微分变分-H半变分不等式解的存在性；微分变分-H半变分不等式的扰动和逼近分析；微分变分-H半变分不等式在非光滑固体和流体力学中的应用研究。.本项目力图在“如何建立微分变分-H半变分不等式解存在性的判别法则？”、“如何揭示微分变分-H半变分不等式关于多参数扰动下解集的本质特征？”、“如何运用项目所建立的理论成果去研究各种非光滑固体和流体力学的前沿问题？”等关键问题的研究中取得实质性进展，从而获得微分变分-H半变分不等式理论和应用方面的一系列创新研究成果。

Differential variational inequality, which was firstly systematically discussed by Professor J.S. Pang and Professor D.E. Stewart in 2008, has attracted considerable attention in the study of mechanical impact problems, economical dynamics, dynamic traffic networks and so forth. However, differential variational inequality as an abstract mathematical model is not applicable for the research on nonsmooth advection-reaction-diffusion problems. To fill this gap, the research project is devoted to systematically investigate a class of differential variational-hemivariational inequalities (DVHVIs, for short), which consists of a variational-hemivariational inequality of parabolic type combined with a nonlinear evolution inclusion. The primary research contents of this project contains the existence of solutions to (DVHVIs), perturbation and approximation analysis for (DVHVIs), and applications in nonsmooth solid and fluid mechanics..In this project we aim to make material improvement in the research on the following key issues: “how to establish the criteria of existence of solutions to (DVHVIs)?”; “how to reveal the essential characteristics of solution set to (DVHVIs) with multi-parameter perturbation?”; “how to apply these theoretical results established in the project to explore various complicated and cutting-edge problems in nonsmooth solid and fluid mechanics?”, etc. A series of innovative research results with respect to theory and various applications of (DVHVIs) is obtained.