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About the kinetic description of fractional diffusion equations modeling chemotaxis. (English) Zbl 1333.35298

Summary: In this paper, we are interested in the microscopic description of fractional diffusion chemotactic models. We will use the kinetic framework of collisional equations having a heavy-tailed distribution as equilibrium state and take an adequate hydrodynamic scaling to deduce the fractional Keller-Segel system for the cell dynamics. In addition, we use this frame to deduce some models for chemotaxis with fractional diffusion including biological effects and non-standard drift terms.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C17 Cell movement (chemotaxis, etc.)
35K55 Nonlinear parabolic equations
35R11 Fractional partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
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