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- W2288394564 abstract "We consider a new class of first order evolutionary variational-hemivariational inequalities for which we prove an existence and uniqueness result. The proof is based on a time-discretization method, also known as the Rothe method. It consists of considering a discrete version of each inequality in the class, proving its unique solvability, and recovering the solution of the continuous problem as the time step converges to zero. Then we introduce a quasi-static frictionless problem for Kelvin--Voigt viscoelastic materials in which the contact is modeled with a nonmonotone normal compliance condition and a unilateral constraint. We prove the variational formulation of the problem cast in the abstract setting of variational-hemivariational inequalities, with a convenient choice of spaces and operators. Further, we apply our abstract result in order to prove the unique weak solvability of the problem." @default.
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- W2288394564 date "2016-01-01" @default.
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- W2288394564 title "The Rothe Method for Variational-Hemivariational Inequalities with Applications to Contact Mechanics" @default.
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- W2288394564 doi "https://doi.org/10.1137/151005610" @default.
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