Finite-time stabilization for bilinear reaction diffusion equation

Abstract

This paper investigates the finite-time stabilization of the bilinear reaction-diffusion equation. Here the reaction term leads to an unbounded control operator. We will first investigate the well-posedness of the system at hand and then proceed to the question of finite-time extinction with feedback control. Our approach is based on the theory of maximal monotone operators. A numerical example is also presented.