Saddle-point structure of fixed points in a reaction-diffusion equation with discontinuous nonlinearity

Fuente: arXiv
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Main Author: Valero, José
Format: Preprint
Published: 2025
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_version_ 1866915417618907136
author Valero, José
author_facet Valero, José
contents In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac delta distribution, we analyze the stability of the stationary solutions and demonstrate that they exhibit a saddle-point structure. As a result, we establish the hyperbolicity of the fixed points.
format Preprint
id arxiv_https___arxiv_org_abs_2507_22452
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Saddle-point structure of fixed points in a reaction-diffusion equation with discontinuous nonlinearity
Valero, José
Dynamical Systems
37B25, 35B35, 35B40, 35B41, 35K55, 58C06
In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac delta distribution, we analyze the stability of the stationary solutions and demonstrate that they exhibit a saddle-point structure. As a result, we establish the hyperbolicity of the fixed points.
title Saddle-point structure of fixed points in a reaction-diffusion equation with discontinuous nonlinearity
topic Dynamical Systems
37B25, 35B35, 35B40, 35B41, 35K55, 58C06
url https://arxiv.org/abs/2507.22452