We are interested in the uniqueness of solutions of a nonlinear, pseudomonotone, stochastic diffusion evolution problem with homogeneous Dirichlet boundary conditions with reflection, where the noise term is additive and given by a stochastic It\^o integral with respect to a Hilbert space valued cylindrical Wiener process. In fact, since there is no It\^o formula available for a solution in general, a general uniqueness result seems not to be available. Nevertheless, assuming more regularity for the solutions or the reflection, we may show some comparison principles.
Niklas Sapountzoglou (Fri,) studied this question.