An Optimal Control Problem for a Class of Degenerate Equations

摘要

A modified initial value problem for a first order operator-differential equation not resolved with respect to the derivative is considered. For the existence of a solution to this problem, unlike a Cauchy problem, one does not need to impose the compatibility conditions on the initial data and the nonhomogeneous right-hand side of the equation. This allows one to extend the space of control functions in the minimization of a quadratic functional over the solutions of the initial value problem. The abstract results are applied to the study of an optimal control problem for a class of PDEs.