Orbital stability of monostable waves for reaction-diffusion systems
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918357533458432 |
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| author | Garénaux, Louis |
| author_facet | Garénaux, Louis |
| contents | We study stability of monostable waves for reaction-diffusion systems. When the solution is initially close to a fast wave profile in optimal topology, we prove convergence to a shifted profile. The proof relies on explicit resolvent kernels estimates, allowing to handle weakly localized perturbations. It allows phase shift construction even when the translational eigenvalue is not associated to a zero of the Evans function.
We further discuss distinction between Evans and Fourier eigenmodes when the marginal group velocity are directed towards the wave interface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22907 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbital stability of monostable waves for reaction-diffusion systems Garénaux, Louis Analysis of PDEs 35B35, 35B40, 35C07, 35K40, 35K57, 35P15 We study stability of monostable waves for reaction-diffusion systems. When the solution is initially close to a fast wave profile in optimal topology, we prove convergence to a shifted profile. The proof relies on explicit resolvent kernels estimates, allowing to handle weakly localized perturbations. It allows phase shift construction even when the translational eigenvalue is not associated to a zero of the Evans function. We further discuss distinction between Evans and Fourier eigenmodes when the marginal group velocity are directed towards the wave interface. |
| title | Orbital stability of monostable waves for reaction-diffusion systems |
| topic | Analysis of PDEs 35B35, 35B40, 35C07, 35K40, 35K57, 35P15 |
| url | https://arxiv.org/abs/2602.22907 |