Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912665944719360 |
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| author | Ciotir, Ioana Goreac, Dan Tölle, Jonas M. |
| author_facet | Ciotir, Ioana Goreac, Dan Tölle, Jonas M. |
| contents | This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the stochastic porous medium equation, stochastic fast- and super fast-diffusion equations, self-organized criticality, stochastic singular $p$-Laplace equations, and the stochastic total variation flow, among others. We present several different notions of solutions, results on convergence of solutions depending on a parameter, and homogenization. Furthermore, we provide some references hinting at the recent progress in regularity results, long-time behavior, ergodicity, and numerical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases Ciotir, Ioana Goreac, Dan Tölle, Jonas M. Probability Numerical Analysis Analysis of PDEs Dynamical Systems Functional Analysis Primary: 35B27, 35K59, 35K65, 35K67, 35K92, 35R60, 37A25, 60H15, 76S05. Secondary: 35A35, 35B35, 47D07, 47J20, 60G15 This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the stochastic porous medium equation, stochastic fast- and super fast-diffusion equations, self-organized criticality, stochastic singular $p$-Laplace equations, and the stochastic total variation flow, among others. We present several different notions of solutions, results on convergence of solutions depending on a parameter, and homogenization. Furthermore, we provide some references hinting at the recent progress in regularity results, long-time behavior, ergodicity, and numerical analysis. |
| title | Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases |
| topic | Probability Numerical Analysis Analysis of PDEs Dynamical Systems Functional Analysis Primary: 35B27, 35K59, 35K65, 35K67, 35K92, 35R60, 37A25, 60H15, 76S05. Secondary: 35A35, 35B35, 47D07, 47J20, 60G15 |
| url | https://arxiv.org/abs/2510.20471 |