Preprint
Aug 2026
A Stochastic Flow for the Stochastic Allen-Cahn Equation with Multiplicative Noise
We establish the existence of a stochastic flow on $L^{\infty} (\mathbb{T})$ for the stochastic Allen-Cahn equation with multiplicative noise \[ (\partial_t - \partial_x^2) u = u - u^3 + \sigma (u) \xi \quad \text{on} \quad \mathbb{R}_+ \times \mathbb{T}, \] where $\xi$ is space-time white noise and $\sigma : \mathbb{R...
S. Esquivel, Hendrik Weber
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