A nonlinear stochastic diffusion-convection equation with reflection
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929643959877632 |
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| author | Sapountzoglou, Niklas Tahraoui, Yassine Vallet, Guy Zimmermann, Aleksandra |
| author_facet | Sapountzoglou, Niklas Tahraoui, Yassine Vallet, Guy Zimmermann, Aleksandra |
| contents | We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a stochastic Itô integral with respect to a Hilbert space valued $Q$-Wiener process. We show existence of a solution to the pseudomonotone stochastic diffusion-convection equation with non-negative initial value as well as the existence of a reflection measure which prevents the solution from taking negative values. In order to show a minimality condition of the measure, we study the properties of quasi everywhere defined representatives of the solution with respect to parabolic capacity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A nonlinear stochastic diffusion-convection equation with reflection Sapountzoglou, Niklas Tahraoui, Yassine Vallet, Guy Zimmermann, Aleksandra Analysis of PDEs Probability 35K86, 60H15, 35K55 We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a stochastic Itô integral with respect to a Hilbert space valued $Q$-Wiener process. We show existence of a solution to the pseudomonotone stochastic diffusion-convection equation with non-negative initial value as well as the existence of a reflection measure which prevents the solution from taking negative values. In order to show a minimality condition of the measure, we study the properties of quasi everywhere defined representatives of the solution with respect to parabolic capacity. |
| title | A nonlinear stochastic diffusion-convection equation with reflection |
| topic | Analysis of PDEs Probability 35K86, 60H15, 35K55 |
| url | https://arxiv.org/abs/2412.16413 |