A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866915738088898560 |
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| author | Alfaro, Matthieu Chainais-Hillairet, Claire Nabet, Flore |
| author_facet | Alfaro, Matthieu Chainais-Hillairet, Claire Nabet, Flore |
| contents | In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12909 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges Alfaro, Matthieu Chainais-Hillairet, Claire Nabet, Flore Analysis of PDEs In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum. |
| title | A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.12909 |