Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy P.O. Box 68-1, 400110 Cluj-Napoca, Romania; Faculty of Mathematics and Computer Science, Babes-Bolyai University Kogalniceanu street, no. 1, 400084, Cluj-Napoca, Romania
We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and an obstacle, the so-called foundation. The material's behavior is modelled with a constitutive law with long memory. The contact is with normal compliance, unilateral constraint, memory effects and adhesion. We present the classical formulation of the problem, then we derive its variational formulation and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities and fixed point.
Sofonea, M., & Patrulescu, F. (2014). A Viscoelastic Contact Problem with Adhesion and Surface Memory Effects. Mathematical Modelling and Analysis, 19(5), 607-626. https://doi.org/10.3846/13926292.2014.979334
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