Asymptotic gain results for attractors of semilinear systems

Abstract

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee--Infante equations, for example.

29 pages. Added detailed explanations why we have to work with set-valued semiprocesses (end of Section 2.1 and beginning of Section 3)