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arXiv · 2412.16413

A nonlinear stochastic diffusion-convection equation with reflection

Niklas Sapountzoglou·Yassine Tahraoui·Guy Vallet·Aleksandra Zimmermann
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Abstract

We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a stochastic It\^{o} integral with respect to a Hilbert space valued $Q$-Wiener process. We show existence of a solution to the pseudomonotone stochastic diffusion-convection equation with non-negative initial value as well as the existence of a reflection measure which prevents the solution from taking negative values. In order to show a minimality condition of the measure, we study the properties of quasi everywhere defined representatives of the solution with respect to parabolic capacity.

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Niklas Sapountzoglou, Yassine Tahraoui, Guy Vallet, Aleksandra Zimmermann. 2024-12-21. A nonlinear stochastic diffusion-convection equation with reflection. https://arxiv.org/abs/2412.16413

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