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.

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