Analysis of a dynamic viscoelastic unilateral contact problem with normal damped response

作者：Han, Jiangfeng^*; Migorski, Stanislaw; Zeng, Huidan

来源：Nonlinear Analysis: Real World Applications , 2016, 28: 229-250.

DOI：10.1016/j.nonrwa.2015.10.004

• Dynamic
• Variational-hemivariational inequality
• Kelvin-Voigt law
• Clarke subdifferential
• Unique solvability

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.

• 出版日期2016-4
• 单位广西财经学院