, Volume 118, Issue 2, pp 429-461

The Carleman Inequality and Its Application to Periodic Optimal Control Governed by Semilinear Parabolic Differential Equations

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Abstract

This paper deals with optimal control problems for semilinear parabolic differential equations, which may be governed by nonmonotone operators and have no global solution, with periodic inputs. The Pontryagin maximum principle is obtained and the Carleman inequality for the backward linearized adjoint system associated with the state system is established.