Variational Analysis of a Dynamic Thermoviscoelastic Unilateral Contact Problem with Normal Damped Response and Friction

Jianwei Hao (), JinRong Wang () and Jiangfeng Han ()
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Jianwei Hao: Guizhou University
JinRong Wang: Guizhou University
Jiangfeng Han: Guangxi University of Finance and Economics

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 2, No 2, 439-465

Abstract: Abstract In this paper, we study a mathematical model that describes the dynamic frictional contact between the thermoviscoelastic body and the foundation. The contact condition is modeled by the so-called nonsmooth interface law involving unilateral constraints and subdifferential inclusions. The weak formulation of our mathematical model is a coupled system containing both parabolic and hyperbolic variational-hemivariational inequalities. As a result, we deliver its unique solvability by employing a surjectivity theorem for pseudomonotone operators, a fixed point argument for history-dependent operators and a mixed equilibrium formulation with suitably selected functions.

Keywords: Dynamic thermoviscoelastic contact problem; Unilateral constraints; Temperature; Variational-hemivariational inequalities; Existence and uniqueness (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02295-0

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