Regularisation by multiplicative noise for reaction-diffusion equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909317919145984 |
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| author | Dareiotis, Konstantinos Holland, Teodor Lê, Khoa |
| author_facet | Dareiotis, Konstantinos Holland, Teodor Lê, Khoa |
| contents | We consider the stochastic reaction-diffusion equation in $1+1$ dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-Hölder space with any regularity index larger than $-1$. We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularisation by multiplicative noise for reaction-diffusion equations Dareiotis, Konstantinos Holland, Teodor Lê, Khoa Probability Analysis of PDEs We consider the stochastic reaction-diffusion equation in $1+1$ dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-Hölder space with any regularity index larger than $-1$. We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution. |
| title | Regularisation by multiplicative noise for reaction-diffusion equations |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2409.11130 |