On global dynamics of reaction--diffusion systems at resonance
Analysis of PDEs
2020-09-24 v2
Abstract
In this paper we use the homotopy invariants methods to study the global dynamics of the reaction-diffusion systems that are at resonance at infinity. Considering degrees of the resonance for the nonlinear perturbation we establish Landesman-Lazer type conditions and use them to express the Rybakowski-Conley index of the invariant set consisting of all bounded solutions. Obtained results are applied to study the existence of solutions connecting stationary points for the system of nonlinear heat equations.
Keywords
Cite
@article{arxiv.1910.12564,
title = {On global dynamics of reaction--diffusion systems at resonance},
author = {Piotr Kokocki},
journal= {arXiv preprint arXiv:1910.12564},
year = {2020}
}
Comments
27 pages