State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities

Samir Adly (), Tahar Haddad () and Ba Khiet Le ()
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Samir Adly: Université de Limoges
Tahar Haddad: Université de Jijel
Ba Khiet Le: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 2, No 2, 473-493

Abstract: Abstract This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion called hypomonotonicity-like of the normal cone to the moving set, which is satisfied by many important cases. Combining this latter notion with an adapted Moreau’s catching-up algorithm and a Cauchy technique, we obtain the strong convergence of approximate solutions to the unique solution, which is a fundamental property. Using standard tools from convex analysis, we show the equivalence between this implicit state-dependent sweeping processes and quasistatic evolution quasi-variational inequalities. As an application, we study the state-dependent quasistatic frictional contact problem involving viscoelastic materials with short memory in contact mechanics.

Keywords: Moreau’s sweeping process; Evolution variational inequalities; Unilateral constraints; Quasistatic frictional contact problems; 49J40; 47J20; 47J22; 58E35; 74M15; 74M10; 74G25 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1427-x

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