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

[摘要] In this work, we present results on stability and hyperbolicity of equilibria for a scalar nonlocal onedimensional quasilinear parabolic problem. We show that this nonlocal version of the well-known ChafeeInfante equation bears some resemblance with the local version. However, its nonlocal characteristic requires a fine analysis of the spectrum of the associated linear operators, a lot more elaborated than the local case. The saddle point property of equilibria is shown to hold for this quasilinear model. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-05

[关键词] Quasilinear problem;Nonlocal operator;Spectral analysis;Hyperbolicity