On effects of sampling radius for the nonlocal Patlak-Keller-Segel chemotaxis model
نویسندگان
چکیده
منابع مشابه
A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
A finite volume method is presented to discretize the Patlak-Keller-Segel (PKS) model for chemosensitive movements. On the one hand, we prove existence and uniqueness of a numerical solution to the proposed scheme. On the other hand, we give a priori estimates and establish a threshold on the initial mass, for which we show that the numerical approximation convergences to the solution to the PK...
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 کاملLocal Discontinuous Galerkin Method for the Keller-Segel Chemotaxis Model
In this paper, we apply the local discontinuous Galerkin (LDG) method to 2D Keller– Segel (KS) chemotaxis model. We improve the results upon (Y. Epshteyn and A. Kurganov, SIAM Journal on Numerical Analysis, 47 (2008), 368-408) and give optimal rate of convergence under special finite element spaces. Moreover, to construct physically relevant numerical approximations, we develop a positivity-pre...
متن کاملConvergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak-Keller-Segel Model
Abstract. Variational steepest descent approximation schemes for the modified Patlak-KellerSegel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recov...
متن کاملFunctional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
We investigate the long time behavior of the critical mass Patlak-Keller-Segel equation. This equation has a one parameter family of steady-state solutions ̺λ, λ > 0, with thick tails whose second moment is not bounded. We show that these steady state solutions are stable, and find basins of attraction for them using an entropy functional Hλ coming from the critical fast diffusion equation in R ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2014
ISSN: 1078-0947
DOI: 10.3934/dcds.2014.34.4911