A quasistatic contact problem for viscoelastic materials with friction and damage |
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Authors: | Yunxiang Li Zhenhai Liu |
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Institution: | a Department of Mathematics of Central South University, Changsha, Hunan 410075, PR China b Department of Mathematics of Hunan City University, Yiyang, Hunan 413000, PR China c School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, PR China |
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Abstract: | We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is quasistatic, the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions. The mechanical damage of the material is described by the damage function, which is modelled by a nonlinear partial differential equation. We derive the variational formulation of the problem, which is a coupled system of a hemivariational inequality and a parabolic equation. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of abstract stationary inclusion and a fixed point theorem. |
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Keywords: | 35B25 35H30 35J32 |
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