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arXiv · 2504.03417

Uniqueness results of a nonlinear stochastic diffusion-convection equation with reflection

Niklas Sapountzoglou
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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.

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Niklas Sapountzoglou. 2025-04-04. Uniqueness results of a nonlinear stochastic diffusion-convection equation with reflection. https://arxiv.org/abs/2504.03417

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