Local Null Controllability of a Chemotaxis System of Parabolic-Elliptic Type

TL;DR

This paper proves the local null controllability of a chemotaxis system of parabolic-elliptic type by linearizing the nonlinear equations, offering a novel approach different from traditional methods for coupled parabolic systems.

Contribution

It introduces a new method of linearizing coupled parabolic-elliptic systems to establish controllability, bypassing challenges posed by nonlinear drift terms.

Findings

Successfully linearized the nonlinear system into two separate linear equations.

Established local null controllability for the original nonlinear chemotaxis system.

Presented a novel approach differing from traditional methods for coupled parabolic systems.

Abstract

In this paper, we are concerned with the controllability of a chemotaxis system of parabolic-elliptic type. By linearizing the nonlinear system into two separated linear equations to bypass the obstacle caused by the nonlinear drift term, we establish the local null controllability of the original nonlinear system. The approach is different from the usual way of treating the coupled parabolic systems.