A Nonlinear Mechanism for Transient Anomalous Diffusion

Abstract: Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local models. This paper investigates a nonlinear diffusion equation where the diffusion coefficient is linearly dependent on concentration. We demonstrate through a perturbative analysis that this physically-grounded model exhibits transient anomalous diffusion. The system displays a clear crossover from an initial subdiffusive regime to standard Fickian behavior at long times. This result establishes an important mechanism for trasient anomalous diffusion that arises purely from local interactions, providing an intuitive alternative to models based on fractional calculus or non-local memory effects.