Dynamics and differential equations that involve inequalities arise where there are hard constraints, such as in mechanical impact, ideal diodes in electrical circuits, and traffic networks. Different frameworks have been proposed for many of these problems; here we will use differential complementarity problems and differential variational inequalities. Most of the differential equations are ordinary differential equations, but mechanical impact leads to partial differential equations, where the technical issues are more difficult.
Questions of existence and uniqueness will be posed and (partially)
answered along with questions are still open. Phenomena such as
Zeno-type solutions and reverse-Zeno solutions are crucial for
understanding the behaviour of these systems.
After completing his degrees (BSc(Math), BE (Elec), PhD (Math)) at the
University of Queensland, David Stewart worked in postdoctoral positions
at the Australian National University, and Texas A&M University (College
Station). David obtained a tenure-track position at the University of
Iowa (Iowa City), and while there rose to the level of Full Professor.
His research interests include dynamics and differential equations,
optimization, and computational mathematics. He has authored and
co-authored several books including "Dynamics with Inequalities: impacts
and hard constraints" (SIAM, 2011).