Global attractor of a PDE model for the kinetics of Trichoderma fungi

Abstract

Partial differential equations (PDEs) are essential tools for modeling and understanding complex natural processes, particularly in biology. This research explores the growth of the fungus Trichoderma in the complex structure of soils, focusing on the production of enzymes (cellulase) during substrate degradation. The proposed reaction-diffusion model is spatialized by taking into account the diffusion of each component. We analyze the existence and uniqueness of the solutions of the obtained PDE problems, as well as their asymptotic behavior. Our results reveal the presence of a global attractor, a fundamental feature with essential implications for the long-term behavior of the system. Numerical simulations are used to illustrate the attributes of this global attractor and provide additional information on the dynamic behavior of the system.