Optimal control of hyperbolic H-hemivariational inequalities with state constraints

Abstract

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered. The optimal solutions are obtained. In addition, their approximating problems are also studied.

Optimal control problems for anti‐periodic quasi‐linear hemivariational inequalities

“…Haslinger and Panagiotopoulos [17] proved the existence of optimal control pairs to the coercive hemivariational inequalities and Migórski and Ochal [18] showed the existence of optimal control pairs to the parabolic hemivariational inequalities. Weigang et al [19] considered the optimal control problems for hyperbolic hemivariational inequalities with the state constrains and Parks and Park [20] proved the existence of optimal control pairs to the hyperbolic linear systems. Motivated by their results, we attempt to prove the existence of anti-periodic solutions for hyperbolic quasi-linear hemivariational inequalities (2).…”