A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations

TL;DR

This paper proves that a broad class of nonlinear reaction-diffusion equations remain stable around their attractors even when subjected to disturbances, enhancing understanding of their robustness.

Contribution

It introduces a local input-to-state stability result for nonlinear reaction-diffusion equations concerning their global attractors.

Findings

Established local input-to-state stability for nonlinear reaction-diffusion equations.

Demonstrated robustness of solutions around attractors under disturbances.

Extended stability analysis to a large class of equations.

Abstract

We establish the local input-to-state stability of a large class of disturbed nonlinear reaction-diffusion equations w.r.t. the global attractor of the respective undisturbed system.