Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Minimal time function
  • sweeping process
  • Hamilton-Jacobi inequalities
  • dissipative Lipschitz multifunction

Mathematics Subject Classification

49J21, 49J52, 49J53, 49N60

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Suggested citation

V. Ríos, P. Wolenski. “The Minimal Time Problem of a Sweeping Process with a Discontinuous Perturbation.” Journal of Convex Analysis 32 (2025), No. 3, 801–824. https://doi.org/10.68381/jca32040

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press LLC.