A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise

TL;DR

This paper introduces a variable transformation technique to convert nonlinear stochastic evolution equations with multiplicative noise into deterministic forms, facilitating the analysis of stochastic porous medium equations.

Contribution

The paper presents a novel change of variables approach that simplifies the study of stochastic porous medium equations with multiplicative noise.

Findings

Reduction of stochastic equations to deterministic forms

Enhanced understanding of stochastic porous medium behavior

Potential for broader application to stochastic PDEs

Abstract

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium equation.