Non-Zenoness of a class of differential quasi-variational inequalities

The Zeno phenomenon of a switched dynamical system refers to the infinite number of mode switches in finite time. The absence of this phenomenon is crucial to the numerical simulation of such a system by time-stepping methods and to the understanding of the behavior of the system trajectory. Extending a previous result for a strongly regular differential variational inequality, this paper establishes that a certain class of non-strongly regular differential variational inequalities is devoid of the Zeno phenomenon. The proof involves many supplemental results that are of independent interest. Specialized to a frictional contact problem with local compliance and polygonal friction laws, this non-Zenoness result is of fundamental significance and the first of its kind. This work was based on research partially supported by the National Science Foundation under grants DMS-0508986 and IIS-0413227 awarded to Rensselaer Polytechnic Institute, where the original version of the paper was first written. The revision was based on research partially supported by the National Science Foundation under grant DMS awarded to the University of Illinois at Urbana-Champaign.