Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917535679512576 |
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| author | Milesis, Dionysis Salins, Michael |
| author_facet | Milesis, Dionysis Salins, Michael |
| contents | We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as reversible chemical reaction networks modeled by the mass-action law, and the question of global existence and uniqueness under a mass-control structure has remained open. In this work, we show that stochastically perturbing reaction-diffusion systems with triangular control of mass by suitable multiplicative noise leads to solutions that exist for all time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06645 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass Milesis, Dionysis Salins, Michael Probability Analysis of PDEs 60H15 (Primary), 35R60 (Secondary) We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as reversible chemical reaction networks modeled by the mass-action law, and the question of global existence and uniqueness under a mass-control structure has remained open. In this work, we show that stochastically perturbing reaction-diffusion systems with triangular control of mass by suitable multiplicative noise leads to solutions that exist for all time. |
| title | Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass |
| topic | Probability Analysis of PDEs 60H15 (Primary), 35R60 (Secondary) |
| url | https://arxiv.org/abs/2604.06645 |