# Random separation property for stochastic Allen-Cahn-type equations

@inproceedings{Bertacco2021RandomSP, title={Random separation property for stochastic Allen-Cahn-type equations}, author={Federico Bertacco and Carlo Orrieri and Luca Scarpa}, year={2021} }

We study a large class of stochastic p-Laplace Allen-Cahn equations with singular potential. Under suitable assumptions on the (multiplicative-type) noise we first prove existence, uniqueness, and regularity of variational solutions. Then, we show that a random separation property holds, i.e. almost every trajectory is strictly separated in space and time from the potential barriers. The threshold of separation is random, and we further provide exponential estimates on the probability of…

## References

SHOWING 1-10 OF 28 REFERENCES

Singular stochastic Allen–Cahn equations with dynamic boundary conditions

- MathematicsJournal of Differential Equations
- 2019

Abstract We prove a well-posedness result for stochastic Allen–Cahn type equations in a bounded domain coupled with generic boundary conditions. The (nonlinear) flux at the boundary aims at…

The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property

- Mathematics
- 2017

Abstract We consider the nonlocal Cahn–Hilliard equation with singular potential and constant mobility. Well-posedness and regularity of weak solutions are studied. Then we establish the validity of…

A variational approach to dissipative SPDEs with singular drift

- Mathematics
- 2016

We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift…

Bounded solutions and their asymptotics for a doubly nonlinear Cahn–Hilliard system

- Mathematics
- 2019

In this paper we deal with a doubly nonlinear Cahn–Hilliard system, where both an internal constraint on the time derivative of the concentration and a potential for the concentration are introduced.…

Global solution to the Allen–Cahn equation with singular potentials and dynamic boundary conditions

- Mathematics
- 2012

Abstract We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen–Cahn type equation describing the phenomenon of phase transitions for a material…

A global existence and uniqueness result for a stochastic Allen–Cahn equation with constraint

- Mathematics
- 2017

This paper addresses the analysis of a time noise‐driven Allen-Cahn equation modelling the evolution of damage in continuum media in the presence of stochastic dynamics. The nonlinear character of…

On the Cahn-Hilliard/Allen-Cahn equations with singular potentials

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2019

The purpose of this work is to prove the existence and uniqueness of the solution for a Cahn-Hilliard/Allen-Cahn system with singular potentials (and, in particular, the thermodynamically relevant…

The Cahn–Hilliard–Oono equation with singular potential

- Mathematics
- 2017

We consider the so-called Cahn–Hilliard–Oono equation with singular (e.g. logarithmic) potential in a bounded domain of ℝd, d ≤ 3. The equation is subject to an initial condition and Neumann…

Strong Solutions for Stochastic Partial Differential Equations of Gradient Type

- Mathematics
- 2011

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general…

Existence of nonnegative solutions to stochastic thin-film equations in two space dimensions

- Mathematics
- 2021

We prove the existence of martingale solutions to stochastic thin-film equations in the physically relevant space dimension $d=2$. Conceptually, we rely on a stochastic Faedo-Galerkin approach using…