Exact controllability of a semilinear reaction–diffusion equation governed by a bilinear control. Issue 5 (24th March 2023)

• Record Type: Journal Article
• Authors: Najib, H.; El Ayadi, R.; Ouakrim, Y.; Ouzahra, M.
• Is Part Of: Applicable analysis. Volume 102:Issue 5(2023)
• Page Start: 1414
• Page End: 1438
• Publication Date: 2023-03-24
• Subjects: Semilinear parabolic equation -- approximate controllability -- exact controllability -- bilinear control; 93B03 -- 93B05 -- 35K57 -- 35K58; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1986022
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper investigates the exact controllability of a semilinear reaction–diffusion equation governed by a multiplicative control. Here, the reaction term leads to an unbounded control operator. We will first study the well-posedness and then proceed to the question of exact steering for the system at hand. Our approaches are based on a fixed point argument and the linearization method. The obtained results are further analysed through a numerical example.