Uniform Null Controllability for a Degenerating Reaction-Diffusion System Approximating a Simplified Cardiac Model
For mathematicians studying control of PDEs, this provides a theoretical controllability result for a simplified cardiac model, but the approach is incremental.
The paper proves uniform null controllability for a family of reaction-diffusion systems that approximate a cardiac electrical model, using a single control. The result holds uniformly with respect to a degenerating parameter.
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.