Abstract
An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions.
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