Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications

Abstract

In this paper, we consider an abstract system which consists of a nonlinear differential inclusion and a parabolic hemivariational inequality (DPHVI) in Banach spaces. The objective of this paper is four fold. The first target is to deal with the existence of solutions and the properties which involve the boundedness and continuous dependence results of the solution set to parabolic hemivariational inequality. The second aim is to investigate the existence of mild solutions to DPHVI by means of a fixed point technique. The third one is to study the existence of a pullback attractor for the multivalued processes governed by DPHVI. Finally, the fourth goal is to demonstrate a concrete application of our main results arising from the dynamic thermoviscoelasticity problems.

New discussion on optimal feedback control for Caputo fractional neutral evolution systems governed by hemivariational inequalities

“…Presently, an increasing number of researchers have achieved significant progress in the field of hemivariational inequalities. The study of hemivariational inequality was first undertaken by Panagiotopoulos in 1981, with the aim of addressing the mechanical challenges associated with nonsmooth and nonconvex energy superpotentials [8][9][10][11][12][13]. In an article by Liu [14], the authors studied existence results of quasilinear parabolic hemivariational inequalities.…”

Time Optimal Feedback Control for 3D Navier–Stokes-Voigt Equations

“…For more details, we refer readers to the papers by Refs. [5,[13][14][15][24][25][26][27][28][29][30][31][32][33][34][35].…”

Control systems described by a class of Riemann-Liouville fractional semilinear evolution hemivariational inequalities

“…The hemivariational inequalities have important applications in structural analysis and nonconvex optimization. For more details, the reader is referred to [3,15,19,20,21,23,28,29,33,34,43] and the references therein, where the treatment relies on monotonicity principles, projection arguments, topological methods, and nonsmooth critical point theory.…”

“…Then from, Lemma 3.4, we calculate that the map f → Λ(S(f ), Ψ(f )) is continuous from ω-X φ into ω-L p (J, X). According to ( 12), ( 13), (15), and ( 16), we get Λ(S(f ),…”