Dynamics with Inequalities

Speaker: Professor David Stewart (University of Iowa)

Differential equations cam be combined with complementarity problems and variational inequalities to give dynamic systems whose behavior changes according to whether whether certain constraints are "active". These models can be used for mechanical impact and contact problems, electrical circuits with ideal diodes, and economic models such as traffic flow models where each driver chooses the shortest path based on the current congestion. Fundamental questions of existence of solutions, their uniqueness, and computations have been opened and partly answered. Examples of such simulations will be demonstrated.

After completing all degrees (BSc(Maths), BE (ElecEng), PhD(Maths)) at the University of Queensland, David Stewart spent 3 years at the Australian National University and 2 years at Texas A&M University before obtaining a tenurable position at Virginia Tech. Shortly afterwards he moved to the University of Iowa, where he has been since. His research interests center on optimization, differential equations, and computational mathematics. He is the author or co-author of over 45 papers and 4 books.