Work

A nonlinear stochastic diffusion-convection equation with reflection

Year: 2024

Type: preprint

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 Itô 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2412.16413

Authors: Sapountzoglou, Niklas, Tahraoui, Yassine, Vallet, Guy, Zimmermann, Aleksandra

Institutions: Clausthal University of Technology, Scuola Normale Superiore, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques et de leurs Applications

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft

Awards: G1863584654, G3619456701

OpenAlex ID: W4405765850

Cites:

Cited by: 1

Related to: 10