| Abstract: |
| We present a stochastic Allen-Cahn equation for the dynamics of biomolecular damage and repair. The system is driven by two noise processes: a multiplicative cylindrical Wiener process, modelling continuous background stochastic fluctuations, and a jump-type noise, modelling the abrupt, localised damage induced by external radiotherapy 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, analyse its long-time behaviour, and present some simulations to illustrate how it captures fundamental biological phenomena, such as damage clustering, stress-induced topology perturbations, and damage dynamics.
The works presented in the talk are based on joint collaborations with Andrea Di Primio (Scuola Normale Superiore, Pisa, Italy), Marvin Fritz (University of Vienna, Austria), and
Margherita Zanella (Politecnico di Milano, Italy). |
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