Nonnegative multiplicative controllability for semilinear multidimensional reaction-diffusion equations

TL;DR

This paper demonstrates that it is possible to approximately control multidimensional semilinear reaction-diffusion systems between nonnegative states at any time using multiplicative controls on the reaction coefficient.

Contribution

It introduces a novel approach for controlling reaction-diffusion equations through multiplicative controls, expanding the scope of controllability in nonlinear PDEs.

Findings

Achieved approximate controllability between nonnegative states

Controlled the system at any arbitrary time

Utilized reaction coefficient as a control mechanism

Abstract

In this paper we consider a multidimensional semilinear reaction-diffusion equation and we obtain at any arbitrary time an approximate controllability result between nonnegative states using as control term the reaction coefficient, that is via multiplicative controls.