Two‐dimensional chemotaxis models with fractional diffusion

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Blowup of solutions to generalized Keller–Segel model (2008, background): “Examples of such a reasoning applied to various semilinear models and realized in miscellaneous Banach spaces can be found in [3, 5, 6, 11, 20, 21, 22, 24].”
Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller--Segel equations in the whole space (2013, methodology): “10 Fractional diffusion The Keller-Segel equations have been generalized with the introduction of non-local diffusion [4].”
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].”