主持人：朱升峰 教授

报告内容介绍：
Partial differential equations are widely used in sciences and engineering. Boundary value problems of partial differential equations are usually studied in their weak forms, that also provide foundations for the development of efficient and effective numerical methods. For a complicated application involving nonsmooth, including set-valued relations among physical quantities, the weak form of a boundary value problem is no longer a variational equation; instead, a variational inequality (if the nonsmooth relation is monotone) or a hemivariational inequality (if the nonsmooth relation is nonmonotone) arises. Variational equations, variational inequalities and hemivariational inequalities can be studied in the general framework of variational-hemivariational inequalities. In recent years, modeling, mathematical analysis, and numerical solution of variational-hemivariational inequalities have attracted much attention in the research communities. This talk is devoted to a mathematical theory of stationary variational-hemivariational inequalities. It will begin with a brief discussion of a model variational equation, followed by an extension to sample variational and hemivariational inequalities, and it will focus on the ideas and proofs of well-posedness of variational-hemivariational inequalities. Current status and future directions of research on the numerical solution of variational-hemivariational inequalities will be summarized. The talk will be accessible to anyone with knowledge at college level mathematics.

主讲人介绍：
韩渭敏，复旦大学数学系学士，中国科学院计算中心硕士，美国马里兰大学博士。现为美国爱荷华大学 (The University of Iowa) 数学系教授、Collegiate Fellow；曾任数学系主任。美国数学会会士(Fellow of the American Mathematical Society)。在非线性、非光滑应用问题的建模、理论分析、数值解方面做过开创性和系统性的工作，包括弹塑性变形、接触力学、流体力学等领域里产生的各种形式的变分不等式与半变分不等式的研究。发表论文两百多篇，在Springer等出版社出版专著与教材十三部。其工作在MathSciNet数据库中被引用四千三百多次，在Google Scholar数据库中被引用约一万五千次。