2024/12/27 by De Andrade, Crystianne L., Alexander Kiselev, Kiselev, Alexander A.
Mathematics · Physics and Astronomy · #35K55 #35K57 #35Q92 #92B99 #92C17 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2412.19940
openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Chemotaxis and reactions are fundamental processes in biology, often intricately intertwined. Chemotaxis, in particular, can be crucial in maintaining and accelerating a reaction. In this work, we extend the investigation initiated by kiselev et al. [17] by examining the impact of chemotactic attraction on reproduction and other processes in the context of anomalous diffusion of gamete densities. For that, we consider a partial differential equation, with a single density function, that includes advection, chemotaxis, absorbing reaction, and diffusion, incorporating the fractional Laplacian Λα. The inclusion of the fractional Laplacian is motivated by experimental evidence supporting the efficacy of anomalous diffusion models, particularly in scenarios with sparse targets. The fractional Laplacian accommodates the nonlocal nature of superdiffusion processes, providing a more accurate representation than traditional diffusion models. Our proposed model represents a step forward in refining mathematical descriptions of cellular behaviors influenced by chemotactic cues.