Global solutions to quadratic systems of stochastic reaction-diffusion equations in space-dimension two
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910402473885696 |
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| author | Leocata, Marta Vovelle, Julien |
| author_facet | Leocata, Marta Vovelle, Julien |
| contents | We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {à} la De Giorgi, as in [GoudonVasseur10]. The adaptation of this technique to the stochastic case requires in its final step an $L^2\ln(L^2)$-bound, furnished by an estimate by duality on the entropy inequality, as in [DesvillettesFellnerPierreVovelle07]. In our stochastic context, and similarly to [DebusscheRoselloVovelle2021], we need to solve a backward SPDE to exploit the duality technique |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05360 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global solutions to quadratic systems of stochastic reaction-diffusion equations in space-dimension two Leocata, Marta Vovelle, Julien Analysis of PDEs We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {à} la De Giorgi, as in [GoudonVasseur10]. The adaptation of this technique to the stochastic case requires in its final step an $L^2\ln(L^2)$-bound, furnished by an estimate by duality on the entropy inequality, as in [DesvillettesFellnerPierreVovelle07]. In our stochastic context, and similarly to [DebusscheRoselloVovelle2021], we need to solve a backward SPDE to exploit the duality technique |
| title | Global solutions to quadratic systems of stochastic reaction-diffusion equations in space-dimension two |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.05360 |