It is OK for dynamics to be multivalued and have nonunique solutions: from the leaky bucket ODE to the Conley decomposition and a total Lyapunov function for hybrid dynamics.
Rafal Goebel received his Ph.D. in mathematics in 2000 from the University of Washington. He held postdoctoral positions at the Departments of Mathematics at University of British Columbia and Simon Fraser University in Vancouver, and at the Electrical and Computer Engineering Department of University of California, Santa Barbara. In 2008, he joined the Department of Mathematics and Statistics at Loyola University Chicago. He received the 2009 SIAM Control and Systems Theory Prize and is a co-author of the Hybrid Dynamical Systems: Modeling, Stability, and Robustness book. His interests include convex, nonsmooth, and set-valued analysis; control, including optimal control; hybrid dynamical systems; mountains; and optimization.