Asymptotic gain results for attractors of semilinear systems
Analysis of PDEs
2020-10-21 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1909.06302,
title = {Asymptotic gain results for attractors of semilinear systems},
author = {Jochen Schmid and Oleksiy V. Kapustyan and Sergey Dashkovskiy},
journal= {arXiv preprint arXiv:1909.06302},
year = {2020}
}
Comments
29 pages. Added detailed explanations why we have to work with set-valued semiprocesses (end of Section 2.1 and beginning of Section 3)