Stochastic Allen-Cahn equation with mobility

Abstract

We introduce a class of stochastic Allen-Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the $d$-dimensional torus in the time interval $[0,T]$. Assuming that $d\le 3$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process $u$ in $L^2$ with continuous paths, satisfying almost surely the regularity properties $u\in C([0,T];H^1)$ and $u\in L^2([0,T];H^2)$.

34 pages

References in corpus (3)

• SPDE in Hilbert Space with Locally Monotone Coefficients
• The dynamic ${\Phi }_3^4$ model comes down from infinity
• Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound

Cited by in corpus (1)

• Motion by curvature and large deviations for an interface dynamics on ${\mathbb{Z}}^2$