Well-Posedness of History/State-Dependent Implicit Sweeping Processes

Shengda Zeng () and Emilio Vilches ()
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Shengda Zeng: Yulin Normal University
Emilio Vilches: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 12, 960-984

Abstract: Abstract This paper is devoted to the study of a new class of implicit state-dependent sweeping processes with history-dependent operators. Based on the methods of convex analysis, we prove the equivalence of the history/state dependent implicit sweeping process and a nonlinear differential equation, which, through a fixed point argument for history-dependent operators, enables us to prove the existence, uniqueness, and continuous dependence of the solution in a very general framework. Moreover, we present some new convergence results with respect to perturbations in the data, including perturbations of the associated moving sets. Finally, the theoretical results are applied to prove the well-posedness of a history-dependent quasi-static contact problem.

Keywords: Implicit sweeping process; History-dependent operator; Frictional contact problem; Viscoelastic material; Unilateral constraints; Moreau’s sweeping process; Evolution variational inequality; 49J40; 47J20; 47J22; 35L15; 35L86; 35L87; 74HXX; 74M10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01730-w

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