Large deviation principle for the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise

Abstract

In this work, we consider the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise, which is fractional in time and white in space. We obtain the existence, uniqueness, and Hölder regularity of the solution. Also, using a weak convergence approach, we prove that the law of solution associated with the above equation with a small perturbation satisfies the large deviation principle in the Hölder norm.

Keywords:

• Large deviations
• stochastic partial differential equations
• weak convergence
• uniform Laplace principle

Disclosure statement

No potential conflict of interest was reported by the authors.