Approximate controllability of the semilinear reaction-diffusion equation governed by a multiplicative control

Mohamed Ouzahra

doi:10.3934/dcdsb.2021081

Article Contents

2022, Volume 27, Issue 2: 1075-1090. Doi: 10.3934/dcdsb.2021081

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Approximate controllability of the semilinear reaction-diffusion equation governed by a multiplicative control

Mohamed Ouzahra^,

M2PA Laboratory, ENS, University of Sidi Mohamed Ben Abdellah, P.O. Box 5206, Bensouda, Fès, Morocco

^* Corresponding author: Mohamed Ouzahra
^* Corresponding author: Mohamed Ouzahra

Received: April 2020

Revised: August 2020

Early access: March 2021

Published: February 2022

The author is supported by USMBA grant (2020)

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Abstract

In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial state we provide sufficient conditions on the desirable state to be approximately reached within an arbitrarily small time interval. Our approaches are based on linear semigroup theory and some results on uniform approximation with smooth functions.

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Mathematics Subject Classification: Primary: 35K57, 35K58; Secondary: 93C20.

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