We study Escherichia coli chemotaxis behavior in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillates in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes small...

Fokker-Planck systems modeling chemotaxis, haptotaxis and angiogenesis are numerous and have been widely studied. Several results exist that concern the gain of L integrability but methods for proving regularizing effects in L∞ are still very few. Here, we consider a special example, related to the Keller-Segel system, which is both illuminating and singular by lack of diffusion on the second e...

We review the relative entropy method in the context of hyperbolic and diffusive relaxation limits of entropy solutions for various hyperbolic models. The main example consists of the convergence from multidimensional compressible Euler equations with friction to the porous medium equation [7]. With small modifications, the arguments used in that case can be adapted to the study of the diffusiv...

In this paper, we are concerned with the asymptotic behavior of solutions to Cauchy problem (or initial-boundary value problem) one-dimensional Keller–Segel model. For problem, prove that time-asymptotically converge nonlinear diffusion wave whose profile is self-similar solution corresponding parabolic equation, which derived by Darcy's law. consider two cases: Dirichlet boundary condition and...

We study a general class of nonlinear mean field Fokker-Planck equations in relation with an effective generalized thermodynamical formalism. We show that these equations describe several physical systems such as: chemotaxis of bacterial populations, Bose-Einstein condensation in the canonical ensemble, porous media, generalized Cahn-Hilliard equations, Kuramoto model, BMF model, Burgers equati...

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, ...

Abstract. The Keller-Segel model is the classical model for chemotaxis of cell populations. It consists of a drift-diffusion equation for the cell density coupled to an equation for the chemoattractant. Here a variant of this model is studied in one-dimensional position space, where the chemotactic drift is turned off for a limiting cell density by a logistic term and where the chemoattractant ...