Well-posedness of a time discretization scheme for a stochastic p-Laplace equation with Neumann boundary conditions

TL;DR

This paper proves the well-posedness of a semi-implicit time discretization scheme for a stochastic p-Laplace parabolic equation with Neumann boundary conditions, involving nonlinearities and multiplicative noise.

Contribution

It establishes the existence and uniqueness of solutions for a specific numerical scheme applied to a stochastic p-Laplace equation with Neumann boundaries.

Findings

The scheme is well-posed under the given conditions.

The analysis uses the Minty-Browder theorem.

Results support the scheme's stability and reliability.

Abstract

In this contribution, we are interested in the analysis of a semi-implicit time discretization scheme for the approximation of a parabolic equation driven by multiplicative colored noise involving a $p$-Laplace operator (with $p\geq 2$), nonlinear source terms and subject to Neumann boundary conditions. Using the Minty-Browder theorem, we are able to prove the well-posedness of such a scheme.