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arXiv · 2005.07857

Stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem

Alexandre N. Carvalho·Estefani M. Moreira
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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.

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Alexandre N. Carvalho, Estefani M. Moreira. 2020-05-16. Stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem. https://arxiv.org/abs/2005.07857

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