Mathematics Colloquium - Carlos Rautenberg
This event is in the past.
Detroit, MI 48202
Speaker: Professor Carlos Rautenberg, George Mason University
Title: Parabolic Quasi-Variational Inequalities: Applications, Theory and Open Problems
Abstract: Quasi-variational inequalities (QVIs) were introduced by Bensoussan and Lions in the 1970’s, and are generalizations of variational inequalities (VIs) where the associated constraint set is not known a priori. In general, QVIs arise in applications involving partial differential operators and where very nonlinear, nonconvex and nonsmooth phenomena lead to state-dependent constraints. We consider parabolic quasi-variational inequalities (QVIs), with pointwise constraints on function values and its gradient, describing recent mathematical models from physics and biology. Open problems concerning existence of solutions, uniqueness, and differentiability are addressed. A semi-discretization in time is employed for the study of a problem class and the derivation of a solution algorithm. We prove convergence of the discretization scheme, and establish existence, regularity, and the non-decreasing property of the solution. The talk is finalized with a report on numerical tests obtained involving different nonlinearities and types of constraints.