Wave propagation for 1-dimensional reaction-diffusion equations with nonzero random drift
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917222883000320 |
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| author | Guan, Dihang He, Hui Hu, Wenqing Yang, Jiaojiao |
| author_facet | Guan, Dihang He, Hui Hu, Wenqing Yang, Jiaojiao |
| contents | We consider the wave propagation for a reaction-diffusion equation on the real line, with a random drift and Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) type nonlinear reaction. We show that when the average drift is positive, the asymptotic wave fronts propagating to the positive and negative directions are both pushed in the negative direction, leading to the possibility that both wave fronts propagate toward negative infinity. Our proof is based on the Large Deviations Principle for diffusion processes in random environments, as well as an analysis of the Feynman-Kac formula. Such probabilistic arguments also reveal the underlying physical mechanism of the wave fronts formation: the drift acts as an external field that shifts the (quenched) free-energy reference level without altering the intrinsic fluctuation structure of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wave propagation for 1-dimensional reaction-diffusion equations with nonzero random drift Guan, Dihang He, Hui Hu, Wenqing Yang, Jiaojiao Analysis of PDEs Mathematical Physics Probability We consider the wave propagation for a reaction-diffusion equation on the real line, with a random drift and Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) type nonlinear reaction. We show that when the average drift is positive, the asymptotic wave fronts propagating to the positive and negative directions are both pushed in the negative direction, leading to the possibility that both wave fronts propagate toward negative infinity. Our proof is based on the Large Deviations Principle for diffusion processes in random environments, as well as an analysis of the Feynman-Kac formula. Such probabilistic arguments also reveal the underlying physical mechanism of the wave fronts formation: the drift acts as an external field that shifts the (quenched) free-energy reference level without altering the intrinsic fluctuation structure of the system. |
| title | Wave propagation for 1-dimensional reaction-diffusion equations with nonzero random drift |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2512.21906 |