Insights into Nonlinear Diffusion Problems and Implications for Biological Systems
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Date
2025-06-14
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
This thesis aims to study and analyze nonlinear partial differential
equations used in modeling diffusion phenomena in physical and biological
systems. The focus is placed on the porous medium equation, non-divergence
form equations, and reaction-diffusion systems in the context of disease spread.
The research employs mathematical techniques such as Banach's fixed-point
theorem and self-similarity to analyze the existence and behavior of solutions.
The results demonstrate the ability of these models to provide accurate
descriptions of the complex dynamics of natural systems in heterogeneous
environments, enhancing their application in fields such as environmental
pollution monitoring and epidemic spread modeling
Description
Keywords
Nonlinear partial differential equations, diffusion problems, self-similar solutions, existence and uniqueness, biological systems, equilibrium points, basic reproduction number