The fractional Keller–Segel model
By Carlos A. Escudero. 2006
132 citations recorded by the source corpus.
The Keller–Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing-up solutions for large enough initial conditions in dimensions d ≥ 2, but all the solutions are regular in one dimension, a mathematical fact that crucially affects the patterns that can form in the biological system. One of the strongest assumptions of the Keller–Segel model is the diffusive character of the cellular motion, known to be false in many situations. We extend this model to such situations in which the cellular dispersal is better modelled by a fractional operator. We analyse this fractional Keller–Segel model and find that all solutions are again globally bounded in time in one dimension. This fact shows the robustness of the main biological conclusions obtained from the Keller–Segel model.
Subfields: Modeling and Simulation, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/267d76d8b52916ea030b15a0df3047c44d9d8c40
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Citations in the corpus
- The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “The chemotaxis systems have been studied with nonlocal and/or nonlinear diffusion, like [115, 34, 53, 182].”
- Two‐dimensional chemotaxis models with fractional diffusion (2009, background): “Recently, the one-dimensional version of (1) has been studied by Escudero [10]with a motivation stemming from mathematical biology.”
- Blowup of solutions to generalized Keller–Segel model (2008, result): “3) possesses global in time solutions not only in the case of classical Brownian diffusion α = 2 but also in the fractional diffusion case 1 < α < 2 as was shown in Escudero [17].”