Global Attractor for a Reaction-Diffusion Model Arising in Biological Dynamic in 3D Soil Structure

TL;DR

This paper investigates a reaction-diffusion PDE model of microbial activity in 3D soil structures, establishing the existence of a global attractor and illustrating its properties through numerical simulations.

Contribution

It introduces a new PDE model for microbial dynamics in soil and proves the existence and uniqueness of solutions along with the global attractor.

Findings

Existence and uniqueness of solutions established.

Global attractor identified and characterized.

Numerical simulations illustrate the attractor's properties.

Abstract

Partial Differential Equations (PDEs) play a crucial role as tools for modeling and comprehending intricate natural processes, notably within the domain of biology. This research explores the domain of microbial activity within the complex matrix of 3D soil structures, providing valuable understanding into both the existence and uniqueness of solutions and the asymptotic behavior of the corresponding PDE model. Our investigation results in the discovery of a global attractor, a fundamental feature with significant implications for long-term system behavior. To enhance the clarity of our findings, numerical simulations are employed to visually illustrate the attributes of this global attractor.