This paper deals with an evolution inclusion which is an equivalent form of a variational-hemivariational inequality arising in quasistatic contact problems for viscoelastic materials. Existence of a weak solution is proved in a framework of evolution triple of spaces via the Rothe method and the theory of monotone operators. Comments on applications of the abstract result to frictional contact problems are made. The work extends the known existence result of a quasistatic hemivariational inequality by S. Migórski and A. Ochal [SIAM J. Math. Anal., 41 (2009) 1415-1435]. One of the linear and bounded operators in the inclusion is generalized to be a nonlinear and unbounded subdifferential operator of a convex functional, and a smallness condition of the coefficients is removed. Moreover, the existence of a hemivariational inequality is extended to a variational-hemivariational inequality which has wider applications.

中文翻译：

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拟静态变分半不等式的存在性

本文涉及演化包含，它是粘弹性材料的准静态接触问题中引起的变分半变分不等式的等效形式。通过Rothe方法和单调算子理论，在空间三重演化框架中证明了弱解的存在。评论了抽象结果在摩擦接触问题中的应用。这项工作扩展了S.Migórski和A. Ochal [SIAM J. Math。Anal。，41（2009）1415-1435]。包含物中的线性和有界算子之一一般化为凸泛函的非线性和无界次微分算子，并且去除了系数的小条件。此外，