English

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)