Propagation reversal on trees in the large diffusion regime
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929220329930752 |
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| author | Hupkes, Hermen Jan Jukic, Mia |
| author_facet | Hupkes, Hermen Jan Jukic, Mia |
| contents | In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite $k$-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction-diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formula's to bound the thin region in parameter space where the propagation direction undergoes a reversal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Propagation reversal on trees in the large diffusion regime Hupkes, Hermen Jan Jukic, Mia Analysis of PDEs Dynamical Systems In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite $k$-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction-diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formula's to bound the thin region in parameter space where the propagation direction undergoes a reversal. |
| title | Propagation reversal on trees in the large diffusion regime |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2401.12899 |