The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative driftdiffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. It is known that, in two space dimensions, for small initial mass there is global existence of classical ...

In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...

This paper deals with large time behaviors of solutions to a Keller-Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in ...

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 ...

An extension of the Newell-Whitehead-Segel amplitude equation covariant under abritrary rotations is derived systematically by the renormalization group method. Typeset using REVTEX 1 The present day theory of pattern formation to a large degree rests on the derivation and exploitation of amplitude equations. In particular, for the formation of 2-dimensional patterns by spontaneous symmetry bre...

We consider the phenomenon of collapse in the critical Keller–Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fruiting body development and biofilm formation. Also KS describes the collapse of a gas of self-gravitating Brownian particles. We find the fluctuation spectrum around the collapsing family of steady states for these e...

We develop a family of new interior penalty discontinuous Galerkin methods for the Keller-Segel chemotaxis model. This model is described by a system of two nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. It has been recently shown that the convective part of this system is of a mixed hyperbol...

We study the following nonlinear elliptic equation 8 < : u ? u + (e u R e u ? 1 jj) = 0 in ; @u @ = 0 on @; where is a smooth bounded domain in R 2. This equation arises in the study of stationary solutions of a chemotaxis system proposed by Keller and Segel. Under the condition that > jj ? 1 ; 6 = 4m for m = 1; 2; :::, where 1 is the rst (nonzero) eigenvalue of ? under the Neumann boundary con...