English

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

Analysis of PDEs 2025-04-07 v1 Probability

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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Cite

@article{arxiv.2504.03417,
  title  = {Uniqueness results of a nonlinear stochastic diffusion-convection equation with reflection},
  author = {Niklas Sapountzoglou},
  journal= {arXiv preprint arXiv:2504.03417},
  year   = {2025}
}

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10 pages