Stochastic Stefan problem on moving hypersurfaces: an approach by a new framework of nonhomogeneous monotonicity
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912257747714048 |
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| author | Pan, Tianyi Wang, Wei Zhai, Jianliang Zhang, Tusheng |
| author_facet | Pan, Tianyi Wang, Wei Zhai, Jianliang Zhang, Tusheng |
| contents | The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a fixed hypersurface with a new kind of nonhomogeneous monotonicity involving a family of time-dependent operators. This new class of SPDEs is of independent interest and can also be applied to solve many other interesting models such as the stochastic $p$-Laplacian equations, stochastic Allen-Cahn equation and stochastic heat equations on time-dependent domains or hypersurfaces. (Monotone) Operator-valued calculus and geometric analysis of moving hypersurfaces play important roles in the study. Moreover, a forthcoming result on the well-posedness of stochastic 2D Navier-Stokes equation on moving domains is also based on our framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Stefan problem on moving hypersurfaces: an approach by a new framework of nonhomogeneous monotonicity Pan, Tianyi Wang, Wei Zhai, Jianliang Zhang, Tusheng Probability Analysis of PDEs Primary 35R37, Secondary 60H15 The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a fixed hypersurface with a new kind of nonhomogeneous monotonicity involving a family of time-dependent operators. This new class of SPDEs is of independent interest and can also be applied to solve many other interesting models such as the stochastic $p$-Laplacian equations, stochastic Allen-Cahn equation and stochastic heat equations on time-dependent domains or hypersurfaces. (Monotone) Operator-valued calculus and geometric analysis of moving hypersurfaces play important roles in the study. Moreover, a forthcoming result on the well-posedness of stochastic 2D Navier-Stokes equation on moving domains is also based on our framework. |
| title | Stochastic Stefan problem on moving hypersurfaces: an approach by a new framework of nonhomogeneous monotonicity |
| topic | Probability Analysis of PDEs Primary 35R37, Secondary 60H15 |
| url | https://arxiv.org/abs/2503.02314 |