Journal of the
Korean Mathematical Society JKMS

In this paper, we study the optimal control for the damped semilinear hyperbolic systems with unknown parameters $$(C(t)y')'+A_2(t,q)y'+A_1(t,q)y=f(t,q,y,u).$$ We will prove the existence of weak solution of this system and is to find the optimal control pair $(\bar{q},\bar{u})\in Q_{\tau}\times {\mathcal U}_{ad}$ such that $\inf_{u\in {\mathcal U}_{ad}}\sup_{q\in Q_{\tau}}J(q,u)=J(\bar{q},\bar{u}).$

Keywords: optimal control, semilinear hyperbolic systems, cost functional, sufficient conditions

MSC numbers: 49J20, 49J35