Point control of pseudoparabolic problems

A control problem governed by a pseudoparabolic equation onQ = Ω × (0, T) where Ω is an open bounded set inR² orR³ with a smooth boundary is studied. Here the controls are of the formv(x,t) = v(t) δ(x ? a), a ? Ω. It is observed that ifv ? L²(0, T), then the trace of the corresponding solutiony(., T; v) belongs toL²(Ω). Existence, uniqueness, and regularity results are given for the optimal control as well as continuity results with respect to perturbation of the pointa.