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

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 the equation is mainly due to a multivoque maximal monotone operator representing a constraint on the damage variable, which is forced to take physically admissible values. By a Yosida approximation and a time-discretization procedure, we prove a result of global-in-time existence and uniqueness of the solution to the stochastic problem.