Stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem
Dynamical Systems
2020-05-22 v2 Analysis of PDEs
Abstract
In this work, we present results on stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem. We show that this nonlocal version of the well-known Chafee-Infante equation bares some resemblance with the local version. However, its nonlocal characteristc requires a fine analysis of the spectrum of the associated linear operators, a lot more ellaborated than the local case. The saddle point property of equilibria is shown to hold for this quasilinear model.
Keywords
Cite
@article{arxiv.2005.07857,
title = {Stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem},
author = {Alexandre N. Carvalho and Estefani M. Moreira},
journal= {arXiv preprint arXiv:2005.07857},
year = {2020}
}