Optimal Control of History-Dependent Evolution Inclusions with Applications to Frictional Contact

Abstract

In this paper, we study a class of subdifferential evolution inclusions involving historydependent operators. First, we improve an existence and uniqueness theorem and prove the continuous dependence result in the weak topologies. Next, we establish the existence of optimal solution to an optimal control problem for the evolution inclusion. Finally, we illustrate the results by an example of an optimal control of a dynamic frictional contact problem in mechanics, whose weak formulation is the evolution variational inequality.

A New Class of History–Dependent Evolutionary Variational–Hemivariational Inequalities with Unilateral Constraints

“…Operators R 1 , R 2 and S are called history-dependent, for their properties and applications, see e.g. [18,25,29,30,32,40]. The main novelty of the paper is to establish a new result on existence, uniqueness and regularity of solution to the inequality (1.1).…”

Optimal Control Problems for Evolutionary Variational Inequalities with Volterra type Operators

“…Also, such problems appear at the simulation of various problems related to injection molding processes, contact mechanics, etc. (see, e.g., [3]). Furthermore, it has its application in problems from economics, finance, optimization theory, and many others (see, e.g.…”

Boundary optimal control of a dynamic frictional contact problem

“…[8], Liu et al [17], Matei and Micu [18], Migórski and Zeng [28], and Sofonea [37]. On the other hand, mathematical models of contact have been studied, for instance, in [25, 30, 36, 39], and the related results on history‐dependent hemivariational inequalities can be found in [12, 13, 15, 23, 26, 27, 38, 40].…”