Time-dependent inclusions and sweeping processes in contact mechanics
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We consider a class of time-dependent inclusions in Hilbert spaces for which we state and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities, convex analysis and fixed point theory. Then, we use this result to prove the unique weak solvability of a new class of Moreau’s sweeping processes with constraints in velocity. Our results are useful in the study of mathematical models which describe the quasistatic evolution of deformable bodies in contact with an obstacle. To provide some examples, we consider three viscoelastic contact problems which lead to time-dependent inclusions and sweeping processes in which the unknowns are the displacement and the velocity fields, respectively. Then we apply our abstract results in order to prove the unique weak solvability of the corresponding contact problems.
KeywordsNonlinear inclusion Sweeping process Contact problem Unilateral constraint Weak solution
Mathematics Subject Classification49J40 47J20 47J22 34G25 58E35 74M10 74M15 74G25
This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH.
- 8.Han, W., Migórski, S., Sofonea, M. (eds.): Advances in Variational and Hemivariational Inequalities, Advances in Mechanics and Mathematics 33. Springer, New York (2015)Google Scholar
- 14.Moreau, J.J.: Sur l’évolution d’un système élastoplastique. C. R. Acad. Sci. Paris, Sér A-Bn 273, A118–A121 (1971)Google Scholar
- 15.Moreau, J.J.: On unilateral constraints, friction and plasticity. In: Capriz, G., Stampacchia, G. (eds.) New Variational Techniques in Mathemaical Physics, C.I.M.E. II, Ciclo 1973, Edizione Cremonese, Roma, p. 173–322 (1974)Google Scholar