# Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment

## TL;DR

This paper studies the global behavior of a stochastic reaction-diffusion system with linear boundaries, proving existence and uniqueness of solutions using fixed point methods and a priori estimates.

## Contribution

It introduces a comprehensive analysis of the shadow Gierer-Meinhardt system under random environments with general boundary conditions, extending previous deterministic results.

## Key findings

- Established local existence and uniqueness of solutions.
- Proved global existence through a priori estimates.
- Analyzed the impact of multiplicative white noise on system dynamics.

## Abstract

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on a priori estimates of solutions.