Optimal design problems for a dynamic viscoelastic plate. I: Short memory material (Q1904638)

Several optimal control problems with the same state problem -- a pseudohyperbolic variational inequality with a linear operator -- are considered. The control parameters appearing in the coefficients of the variational inequality as well as on the right-hand side are analyzed. The thickness of the dynamic viscoelastic plate with velocity constraints plays the role of control variable. Cost functionals correspond with adjusting the deflection (or the field moments) to a prescribed function \(z_d\) (with minimal cost). Existence of an optimal control is proven on the abstract level. Using the method of penalization an existence and uniqueness theorem for a solution of an initial-boundary value problem for a pseudohyperbolic variational inequality is proved.