Approximate controllability of evolution hemivariational inequalities in Banach spaces.

In this paper, we discuss the approximate controllability of control problems governed by evolution hemivariational inequalities in super-reflexive Banach spaces by preassuming the approximate controllability of the associated linear system. We first show that the original problem is connected with a differential inclusion problem involving the Clarke subdifferential operator, and then we prove the approximate controllability of the original problem via the approximate controllability of the differential inclusion problem. The paper offers a unique solution to a challenge introduced by assuming the underlying space X as a super-reflexive Banach space, which presents issues of convexity due to the nonlinear nature of the duality map involved in the expression of the control. Such issues are not present when X is a separable Hilbert space. Therefore, the paper's novelty is its successful resolution of the convexity problem, paving the way for approximate controllability of the evolution hemivariational inequality in which X is a super-reflexive Banach space. [ABSTRACT FROM AUTHOR]