Journal of the
Korean Mathematical Society JKMS

In this paper, we study optimal control problems for parabolichemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control for various observation cases.

Keywords: hemivariational inequality, existence of solution, boundary stabilization, decay rates

MSC numbers: Primary 49K205; Secondary 93C20