Saddle-point structure of fixed points in a reaction-diffusion equation with discontinuous nonlinearity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915417618907136 |
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| 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 |