Regional Gradient Controllability of Semi-Linear Parabolic Systems

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The purpose of this paper is to study regional gradient controllability for a class of semi-linear distributed parabolic systems. First, we give a definition and delineate some properties of this concept, and we show that under the hypothesis, the approximate regional gradient controllability of semi-linear parabolic system, we find a control which steers a system to a desired gradient in a sub-region of the system domain. At last, we present an approach based on fixed point techniques leading to a numerical approach which is successfully tested through various examples and simulations.
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Template Gradient; Semi-Linear Parabolic Systems; Regional Controllability; Fixed-Point Theorems

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