An Allen-Cahn equation with jump-diffusion noise for biological damage and repair processes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911457304641536 |
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| author | Di Primio, Andrea Fritz, Marvin Scarpa, Luca Zanella, Margherita |
| author_facet | Di Primio, Andrea Fritz, Marvin Scarpa, Luca Zanella, Margherita |
| contents | This paper analyzes a stochastic Allen--Cahn equation for the dynamics of biomolecular damage and repair. The system is driven by two distinct noise processes: a multiplicative cylindrical Wiener process, modeling continuous background stochastic fluctuations, and a jump-type noise, modeling the abrupt, localized damage induced by external shocks. The drift of the equation is singular and covers the typical logarithmic Flory-Huggins potential required in phase-separation dynamics. We prove well-posedness of the model in a strong probabilistic sense, and analyze its long-time behavior in terms of existence and uniqueness of invariant measures, ergodicity, and mixing properties. Eventually, we present an Euler--Maruyama scheme to simulate the model and illustrate how it captures fundamental biological phenomena, such as damage clustering, stress-induced topology perturbations, and damage dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Allen-Cahn equation with jump-diffusion noise for biological damage and repair processes Di Primio, Andrea Fritz, Marvin Scarpa, Luca Zanella, Margherita Probability Analysis of PDEs This paper analyzes a stochastic Allen--Cahn equation for the dynamics of biomolecular damage and repair. The system is driven by two distinct noise processes: a multiplicative cylindrical Wiener process, modeling continuous background stochastic fluctuations, and a jump-type noise, modeling the abrupt, localized damage induced by external shocks. The drift of the equation is singular and covers the typical logarithmic Flory-Huggins potential required in phase-separation dynamics. We prove well-posedness of the model in a strong probabilistic sense, and analyze its long-time behavior in terms of existence and uniqueness of invariant measures, ergodicity, and mixing properties. Eventually, we present an Euler--Maruyama scheme to simulate the model and illustrate how it captures fundamental biological phenomena, such as damage clustering, stress-induced topology perturbations, and damage dynamics. |
| title | An Allen-Cahn equation with jump-diffusion noise for biological damage and repair processes |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2602.17495 |