Regional boundary controllability of the gradient of semi-linear parabolic systems

Abstract

The purpose of this paper is to explore the concept of regional gradient-controllability for semi linear parabolic distributed systems. We are interested in transferring the state gradient of the system to a desired gradient given on the subregion ω or Γ of the whole domain Ω. We give a definition and delineate some properties of this concept, and we show that under some hypothesis, that the approximate regional controllability for the associated linear system holds, we determine the control ensuring the transfer of the system. The approach developed is based on an extension of the method H.U.M and the Schauder fixed point theorem. The developed method lead to an algorithms for constructing the control ensuring the transfer of the system from a desired gradient and we finish by numerical simulation.