The field-road diffusion model: fundamental solution and asymptotic behavior
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912361611264000 |
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| author | Alfaro, Matthieu Ducasse, Romain Tréton, Samuel |
| author_facet | Alfaro, Matthieu Ducasse, Romain Tréton, Samuel |
| contents | We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of different dimensions, with exchange boundary conditions. Despite the intricate geometry of the problem, we provide an explicit expression for its fundamental solution and for the solution to the associated Cauchy problem. The main tool is a Fourier (on the road variable)/Laplace (on time) transform. In addition, we derive estimates for the decay rate of the $L^{\infty}$ norm of these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01859 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The field-road diffusion model: fundamental solution and asymptotic behavior Alfaro, Matthieu Ducasse, Romain Tréton, Samuel Analysis of PDEs We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of different dimensions, with exchange boundary conditions. Despite the intricate geometry of the problem, we provide an explicit expression for its fundamental solution and for the solution to the associated Cauchy problem. The main tool is a Fourier (on the road variable)/Laplace (on time) transform. In addition, we derive estimates for the decay rate of the $L^{\infty}$ norm of these solutions. |
| title | The field-road diffusion model: fundamental solution and asymptotic behavior |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2207.01859 |