Title: Variational-Hemivariational Inequalities: Theory, Numerical Analysis, and Applications

Abstract: In recent years, modeling, mathematical analysis, and numerical solution of hemivariational inequalities, or more generally, variational-hemivariational inequalities, have attracted much attention in the research communities. Through the formulation of variational-hemivariational inequalities, application problems involving nonsmooth, monotone or non-monotone, multivalued constitutive laws, forces, and boundary conditions can be treated successfully. Variational-hemivariational inequalities have been successfully applied in a wide variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics. 

This talk will provide an overview of the mathematical theory and numerical analysis of families of variational-hemivariational inequalities, with applications in solid mechanics and fluid mechanics. It will begin with a brief discussion of a model boundary value problem of an elliptic PDE, and then naturally extend the discussion to sample variational inequalities and hemivariational inequalities. The talk will be accessible to anyone with basic knowledge of PDEs.

Short Bio: Professor Weimin Han conducts research on interdisciplinary applied mathematics with an emphasis on numerical analysis. He is a Fellow of the American Mathematical Society. He was named a Best Mathematics Scientist in the Research.com ranking of top Mathematics scientists, and was named a Highly Ranked Scholar–Lifetime in the Specialty of Numerical Analysis by ScholarGPS, in recognition of his exceptional productivity, noteworthy impact and quality of scholarly work in the top 0.05% of scholars in the Specialty worldwide.