In this paper we study the existence of one and multidimensional traveling wave solutions for general chemotaxis or so-called Keller-Segel models without reproduction of the chemotactic species. We present a constructive approach to give modelers a choice of chemotactic sensitivity functionals, production, and degradation terms for the chemical signal at hand. The main aim is to understand the ...

It has been well established that, in attraction-repulsion Keller–Segel systems of the form$ \begin{equation*} \left\{ \begin{aligned} u_t & = \Delta u - \chi \nabla \cdot (u\nabla v) + \xi w), \\ \tau v_t v \alpha \beta v, w_t w \gamma \delta \end{aligned} \right. \end{equation*} $in a smooth bounded domain $ \Omega \subseteq \mathbb{R}^n $, n\in\mathbb{N} with Neumann boundary conditions ...

We study a kinetic model for chemotaxis introduced by Othmer, Dunbar, and Alt [22], which was motivated by earlier results of Alt, presented in [1], [2]. In two papers by Chalub, Markowich, Perthame and Schmeiser, it was rigorously shown that, in three dimensions, this kinetic model leads to the classical KellerSegel model as its drift-diffusion limit when the equation of the chemo-attractant i...

This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and b...

We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system. Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values. The reliability of HDM...

In this article, Lie and discrete symmetry transformation groups of linear nonlinear Newell-Whitehead-Segel (NWS) equations are obtained. By using these groups, several group invariant solutions considered NWS have been constructed. Furthermore, some more generated by group. Graphical representations obtained also presented.

Chemotaxis of single cells has been extensively studied and a great deal on intracellular signaling and cell movement is known. However, systematic methods to embed such information into continuum PDE models for cell population dynamics are still in their infancy. In this paper, we consider chemotaxis of run-and-tumble bacteria and derive continuum models that take into account of the detailed ...