Optimal control problem for the backward heat equation
Copyright policy )Optimal control problem for the backward heat equation
The optimal control problem of minimizing a quadratic functional for the system described by the Cauchy problem for the backward heat equation in which the control appears in boundary conditions is investigated. Under suitable conditions the existence and uniqueness of the optimal solution is proved. Necessary as well as sufficient conditions for optimality in the form of variational inequalities are obtained. The results generalize investigations in this field and can be applied to a broader class of constraints on the control.
Cauchy problem, optimal control, heat equation, Heat equation, Optimality conditions for problems involving partial differential equations, conditions for optimality, variational inequalities
Cauchy problem, optimal control, heat equation, Heat equation, Optimality conditions for problems involving partial differential equations, conditions for optimality, variational inequalities
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