Coupled reaction-diffusion equations on adjacent domains
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866912413245243392 |
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| author | Berestycki, Henri Rossi, Luca Tellini, Andrea |
| author_facet | Berestycki, Henri Rossi, Luca Tellini, Andrea |
| contents | We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two densities are considered, and an exchange occurs through the separating boundary.
We study the long-time behavior of the solution, and, when it converges to a positive steady state, we prove the existence of an asymptotic speed of propagation in some specific directions. Moreover, we determine how such a speed qualitatively depends with respect to several parameters appearing in the model.
In the case $N=2$, we compare such properties to those studied in [6-9] for a model with a line representing a road of fast diffusion at the boundary of a half-plane, which can be seen as a singular limit of the problem studied here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_11717 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Coupled reaction-diffusion equations on adjacent domains Berestycki, Henri Rossi, Luca Tellini, Andrea Analysis of PDEs 35K57, 35B40, 35K40, 35K45 We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two densities are considered, and an exchange occurs through the separating boundary. We study the long-time behavior of the solution, and, when it converges to a positive steady state, we prove the existence of an asymptotic speed of propagation in some specific directions. Moreover, we determine how such a speed qualitatively depends with respect to several parameters appearing in the model. In the case $N=2$, we compare such properties to those studied in [6-9] for a model with a line representing a road of fast diffusion at the boundary of a half-plane, which can be seen as a singular limit of the problem studied here. |
| title | Coupled reaction-diffusion equations on adjacent domains |
| topic | Analysis of PDEs 35K57, 35B40, 35K40, 35K45 |
| url | https://arxiv.org/abs/1903.11717 |