Generalized solvability and optimal control for an integro-differential equation of a hyperbolic type
Keywords:Integro-differential equation, generalized solvability, optimal control, a priory inequalities, Volterra operator
We consider an integro-differential operator with Volterra type integral term. We provide a priory inequalities in negative norms for certain spaces. Further, using obtained inequalities we prove well-posedness (existence and uniqueness of the (weak) generalized solution) of the corresponding boundary value problem as well as a theorem on optimal control existence.