Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911709176791040 |
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| author | Bouton, Hector Desvillettes, Laurent Dietert, Helge |
| author_facet | Bouton, Hector Desvillettes, Laurent Dietert, Helge |
| contents | We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i Δa\_i = (-1)^i (a\_1 a\_3 - a\_2 a\_4)$, where $a\_i \geq 0$ model the concentrations of chemical species undergoing a chemical reaction and diffusing (each with its diffusion rate $d\_i > 0$) in a bounded container. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_23709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry Bouton, Hector Desvillettes, Laurent Dietert, Helge Analysis of PDEs We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i Δa\_i = (-1)^i (a\_1 a\_3 - a\_2 a\_4)$, where $a\_i \geq 0$ model the concentrations of chemical species undergoing a chemical reaction and diffusing (each with its diffusion rate $d\_i > 0$) in a bounded container. |
| title | Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.23709 |