Abstract
The aim of this paper is to study the constrained gradient controllability problem governed by parabolic evolution equations. The purpose is to find and compute the control u that steers the gradient state from an initial gradient one $$\nabla y_{_{0}}$$ to a gradient vector supposed to be unknown between two defined levels $$\alpha (\cdot )$$ and $$\beta (\cdot )$$ , only on a subregion $$\omega $$ of the system evolution domain $$\varOmega $$ . The obtained results have been proved via two approaches: The first one is based on sub-differential techniques, while the second one is based on Lagrangian multipliers. An algorithm is given on the basis of Uzawa algorithm, and numerical results are established.
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