The goal of this paper is to exhibit a critical mass phenomenon occuring in a model for cell self-organization via chemotaxis. The very well known dichotomy arising in the behavior of the macroscopic Keller-Segel system is derived at the kinetic level, being closer to microscopic features. Indeed, under the assumption of spherical symmetry, we prove that solutions with initial data of large mas...

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions...

Chemotaxis models are based on spatial or temporal gradient measurements by individual organisms. The key contribution of Keller and Segel (J Theor Biol 30:225-234, 1971a; J Theor Biol 30:235-248, 1971b) is showing that erratic measurements of individuals may result in an accurate chemotaxis phenomenon as a group. In this paper we provide another option to understand chemotactic behavior when i...

The existence and nonexistence of global in time solutions is studied for a class of equations generalizing the chemotaxis model of Keller and Segel. These equations involve Lévy diffusion operators and general potential type nonlinear terms.

This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by ( ) ⎧⎨ ⎩ ut = ∇ · ( u∇u √ u2 + |∇u|2 ) − χ∇ · ( u∇v √ 1 + |∇v|2 ) ,

A model for exact sensory adaptation has been published by Segel and co-workers in several papers [e.g., Knox, B. E., Devreotes, P. N., Goldbeter, A. & Segel, L. A. (1986) Proc. Natl. Acad. Sci. USA 83, 2345-2349]. The model comprises a pair of states whose relative probabilities are determined by the binding of a ligand. A second pair of states related by the same ligand binding is accessible ...

In this work, we obtain quantitative convergence of moderately interacting particle systems towards solutions nonlinear Fokker-Planck equations with singular kernels. addition, prove the well-posedness for McKean-Vlasov SDEs involving these kernels and trajectorial propagation chaos associated systems. Our results only require very weak regularity on interaction kernel, including Biot-Savart at...

This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite striking similarity between this and Keller–Segel system, we prove absence finite-time blow-up phenomenon even supercritical case. It means that for any regular initial data, independently magnitude mass, classical solution exists globally time dimensional setting. Moreover, exponential de...

Abstract In this work we introduce semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure. Examples of such equations include linear Fokker–Planck and Keller–Segel equations. The two proposed are first-order accurate in time, explicitly solvable, second-order fourth-order space, which obtained via implementation classical continuous elemen...

The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of generalized nonlinear variant to degenerate Cahn-Hilliard system. This analysis made possible from observation that equivalent relaxed version Furthermore, this latter has an interesting application modelling tissues. Indeed, compressible and incompressible porous medium type e...