2000 character limit reached
Uniqueness results of a nonlinear stochastic diffusion-convection equation with reflection (2504.03417v1)
Published 4 Apr 2025 in math.AP and math.PR
Abstract: 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.