A class of fractional differential hemivariational inequalities with application to contact problem

Abstract

Abstract. In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.Mathematics Subject Classification. 35L15, 35L86, 35L87, 74Hxx, 74M10.

Well-posedness of history-dependent evolution inclusions with applications

“…We refer to [14,17,18,20,28,29,31,33] for various related results on history-dependent inequality problems, and to a recent monograph [32] for a comprehensive research. Moreover, various classes of related differential variational inequalities and differential hemivariational inequalities have been studied only recently in [10][11][12]24,35]. The novelties of the paper are following.…”

Penalty and regularization method for variational‐hemivariational inequalities with application to frictional contact

“…Therefore, by Theorem 9(i), we infer that for each > 0, there exists a unique solution ∈ to the problem ⟨ , − ⟩ + 1 ⟨ , − ⟩ + ( ) − ( ) + 0 ( ; − ) ≥ ⟨ , − ⟩ for all ∈ . Using the inequality (45) and notation (37), (39) and (42), we deduce that that ∈ is a solution to Problem 22. The uniqueness of solution to Problem 22 is proved analogously, as the one to Problem 18, and therefore its proof is omitted.…”

“…It has started with the works of Panagiotopoulos, see [25,26] and has been substantially developed during the last thirty years. The mathematical results on hemivariational and variational-hemivariational inequalities have found numerous applications to mechanics, physics and engineering, see [10,[16][17][18]20,21,24,[32][33][34][35][37][38][39] and the references therein.…”

Gap Functions and Error Bounds for Variational–Hemivariational Inequalities

“…The theory of variational-hemivariational inequalities has been extensively studied by many authors in different directions, and it has found various applications in mechanics, engineering, especially in optimization and nonsmooth analysis. Recent existence results for variational-hemivariational inequalities can be found, in e.g., [16, 31, 33-41, 43, 47, 48], the stability in the sense of convergence and the well-posedness, in e.g., [18,30,32,[50][51][52][53], and the computational issues have been addressed in, e.g., [15,17].…”