منابع مشابه
The fractional Keller-Segel model
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...
متن کاملRefined hyper-contractivity and uniqueness for the Keller-Segel equations
Article history: Received 16 January 2014 Accepted 20 September 2014 Available online 22 October 2014 Submitted by Y. Wei MSC: 15A18 15A57
متن کاملA stochastic Keller-Segel model of chemotaxis
We introduce stochastic models of chemotaxis generalizing the deterministic KellerSegel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean’s approach, we derive the exact kinetic equation satisfied by the density distribution of cells. In the mean field limit where statistical correlations between cell...
متن کاملThe Keller-Segel model with small diffusivity
We study the classical model for chemotaxis, the so-called Keller-Segel model, which is a drift-diffusion equation for the cell density coupled with an elliptic equation describing the evolution of the chemoattractant. We investigate the case of small cell diffusivity and, in particular, the hyperbolic limit of the system as the diffusion coefficient goes to zero. Considering a model where the ...
متن کاملKeller-Segel, Fast-Diffusion and Functional Inequalities
We will show how the critical mass classical Keller-Segel system and the critical displacement convex fast-diffusion equation in two dimensions are related. On one hand, the critical fast diffusion entropy functional helps to show global existence around equilibrium states of the critical mass Keller-Segel system. On the other hand, the critical fast diffusion flow allows to show functional ine...
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ژورنال
عنوان ژورنال: Séminaire Laurent Schwartz — EDP et applications
سال: 2018
ISSN: 2266-0607
DOI: 10.5802/slsedp.126