On a stochastic phase-field model of cell motility with singular diffusion
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915719269056512 |
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| author | Saef, Amjad Stannat, Wilhelm |
| author_facet | Saef, Amjad Stannat, Wilhelm |
| contents | We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a phase-field. We investigate both the case of an independently evolving phase-field and of coupled phase-field evolution driven by a viscous Hamilton-Jacobi equation. Such systems are used in the modelling of single-cell chemotaxis, where the contour of the cell shape corresponds to a level set of the phase-field. The technical challenge lies in the singularities at zero level sets of the phase-field. For large classes of initial data, we establish global existence of probabilistically weak solutions in $L^2$-spaces with weights which compensate for the singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05881 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a stochastic phase-field model of cell motility with singular diffusion Saef, Amjad Stannat, Wilhelm Probability Analysis of PDEs 35K55, 60H15, 80A22, 92C17, 92D25 We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a phase-field. We investigate both the case of an independently evolving phase-field and of coupled phase-field evolution driven by a viscous Hamilton-Jacobi equation. Such systems are used in the modelling of single-cell chemotaxis, where the contour of the cell shape corresponds to a level set of the phase-field. The technical challenge lies in the singularities at zero level sets of the phase-field. For large classes of initial data, we establish global existence of probabilistically weak solutions in $L^2$-spaces with weights which compensate for the singularities. |
| title | On a stochastic phase-field model of cell motility with singular diffusion |
| topic | Probability Analysis of PDEs 35K55, 60H15, 80A22, 92C17, 92D25 |
| url | https://arxiv.org/abs/2601.05881 |