Stability of travelling wave solutions to reaction-diffusion equations driven by additive noise with Hölder continuous paths
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918278405816320 |
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| author | Saef, Amjad Stannat, Wilhelm |
| author_facet | Saef, Amjad Stannat, Wilhelm |
| contents | In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with Hölder continuous paths, covering in particular fractional Brownian motion with general Hurst index. We obtain long- and short time asymptotic error bounds on the maximal distance from the solution of the stochastic reaction-diffusion equation to the orbit of travelling wave fronts. These bounds, in terms of Hurst index and Hölder exponent, apply to a large class of infinite-dimensional self-similar drivers with Hölder continuous paths, such as linear fractional stable motion. We find that for short times, higher Hurst indices imply higher stability, while for large times, a smaller gap between Hurst index and Hölder exponent implies stability for larger noise amplitudes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of travelling wave solutions to reaction-diffusion equations driven by additive noise with Hölder continuous paths Saef, Amjad Stannat, Wilhelm Probability Dynamical Systems 35K57, 60G22, 60H15, 92C20 In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with Hölder continuous paths, covering in particular fractional Brownian motion with general Hurst index. We obtain long- and short time asymptotic error bounds on the maximal distance from the solution of the stochastic reaction-diffusion equation to the orbit of travelling wave fronts. These bounds, in terms of Hurst index and Hölder exponent, apply to a large class of infinite-dimensional self-similar drivers with Hölder continuous paths, such as linear fractional stable motion. We find that for short times, higher Hurst indices imply higher stability, while for large times, a smaller gap between Hurst index and Hölder exponent implies stability for larger noise amplitudes. |
| title | Stability of travelling wave solutions to reaction-diffusion equations driven by additive noise with Hölder continuous paths |
| topic | Probability Dynamical Systems 35K57, 60G22, 60H15, 92C20 |
| url | https://arxiv.org/abs/2501.12944 |