Uniform Null Controllability for a Degenerating Reaction-Diffusion System Approximating a Simplified Cardiac Model

TL;DR

This paper proves that a family of nonlinear reaction-diffusion systems, modeling cardiac electrical activity, can be uniformly controlled to zero regardless of a degenerating parameter, using advanced mathematical techniques.

Contribution

It establishes uniform null controllability for a class of nonlinear systems approximating cardiac models, a novel result in the control of degenerating reaction-diffusion systems.

Findings

Uniform null controllability achieved for all parameter values

Control implemented via a single control input

Method combines Carleman estimates and energy inequalities

Abstract

This paper is devoted to the analysis of the uniform null controllability for a family of nonlinear reaction-diffusion systems approximating a parabolic-elliptic system which models the electrical activity of the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by means of a single control is shown. The proof is based on the combination of Carleman estimates and weighted energy inequalities.