Abstract
In this paper, we find the necessary conditions for optimality in distributed control problem for semilinear elliptic control problem Governed by elliptic operator of infinite order with finite dimension. First order and second order sufficient optimality conditionare obtained for this control problem using Theorems (14).
Highlights
It is known that in the case of nonlinear equations the first order conditions are not in general sufficient for optimality
In this paper we are going to drive a second order sufficient optimality condition for a class of semilinear elliptic control problems governed by elliptic operator of infinite order with finite dimension
Gali et al [10] presented a set of inequalities defining an optimal control of a system governed by self-adjoint elliptic operators with an infinite number of variables
Summary
It is known that in the case of nonlinear equations the first order conditions are not in general sufficient for optimality. In this paper we are going to drive a second order sufficient optimality condition for a class of semilinear elliptic control problems governed by elliptic operator of infinite order with finite dimension. Gali et al [10] presented a set of inequalities defining an optimal control of a system governed by self-adjoint elliptic operators with an infinite number of variables. In the present paper, using the Theory of [16], [14, 15] and [2, 3, 4] we derive the necessary conditions of optimality for control problem governed by semilinear elliptic operator.
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