Analysis of a dynamic viscoelastic unilateral contact problem with normal damped response |
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| Affiliation: | 1. Faculty of Mathematics and Computer Science, Jagiellonian University, Institute of Computer Science, ul. Łojasiewicza 6, 30-348 Krakow, Poland;2. Department of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, PR China;1. Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou, China;2. CIDMA, Department of Mathematics, University of Aveiro, Portugal;3. Department of Mathematics, Fujian Normal University, Fuzhou, China;1. College of Science, Qilu University of Technology, Jinan 250353, China;2. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China;1. LAboratoire de Mathématiques, Physique et Systèmes (LAMPS), Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France;2. Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30348 Krakow, Poland;1. College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;2. Department of Mathematics, University of Iowa, Iowa City, IA 52242-1410, USA;3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;4. Faculty of Mathematics and Computer Science, Jagiellonian University, Institute of Computer Science, ul. Stanisława Łojasiewicza 6, 30348 Krakow, Poland;5. Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan, France |
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| Abstract: | In this paper we deal with a viscoelastic unilateral contact problem with normal damped response. The process is assumed to be dynamic and frictionless. Normal damping function is modeled by the Clarke subdifferential of a nonconvex and nonsmooth function. First, the variational formulation of this problem is provided in the form of a nonlinear first order variational–hemivariational inequality for the velocity field. Then, based on the surjectivity results for pseudomonotone and maximal monotone operators, we obtain the unique solvability for a new class of abstract evolutionary variational-hemivariational inequalities. Finally, we apply our abstract results to prove the existence of a unique weak solution to the corresponding contact problem. |
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| Keywords: | Dynamic Variational-hemivariational inequality Kelvin–Voigt law Clarke subdifferential Unique solvability |
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