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arXiv · 1512.08736

Stochastic Allen-Cahn equation with mobility

Lorenzo Bertini·Paolo Buttà·Adriano Pisante
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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 $u\in L^2([0,T];H^2)$.

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Lorenzo Bertini, Paolo Buttà, Adriano Pisante. 2015-12-29. Stochastic Allen-Cahn equation with mobility. https://doi.org/10.1007/s00030-017-0477-3

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