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Partial Differential Equations (PDEs) play a crucial role as tools formodeling and comprehending intricate natural processes, notably within thedomain of biology. This research explores the domain of microbial activitywithin the complex matrix of 3D soil structures, providing valuableunderstanding into both the existence and uniqueness of solutions and theasymptotic behavior of the corresponding PDE model. Our investigation resultsin the discovery of a global attractor, a fundamental feature with significantimplications for long-term system behavior. To enhance the clarity of ourfindings, numerical simulations are employed to visually illustrate theattributes of this global attractor.

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