Journal of Convex Analysis 32 (2025), No. 3, 801--824
Copyright Heldermann Verlag 2025
The Minimal Time Problem of a Sweeping Process with a Discontinuous Perturbation
Vinicio Ríos
Department of Mathematics, Louisiana State University, Baton Rouge, U.S.A.
vrios3@lsu.edu
Peter Wolenski
Department of Mathematics, Louisiana State University, Baton Rouge, U.S.A.
pwolens@lsu.edu
We investigate the minimal time problem where the dynamic data involves an autonomous sweeping process perturbed by a discontinuous dissipative Lipschitz multifunction. We show that under mild assumptions the minimal time function can be characterized in terms of Hamilton-Jacobi inequalities, one of which incorporates a limiting component that captures the discontinuous nature of the perturbation. Continuity of the minimal time function is proven under a Petrov-type condition.
Keywords: Minimal time function, sweeping process, Hamilton-Jacobi inequalities, dissipative Lipschitz multifunction.
MSC: 49J21, 49J52, 49J53, 49N60.
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