Mathematical modelling of chemotaxis (the movement of biological cells or organisms in
response to chemical gradients) has developed into a large and diverse discipline, whose …

This article summarites various aspects and results for some general formulations of the
classical chemotaxis models also known as Keller-Segel models. It is intended as a survey …

We recount and discuss some of the most important methods and blow-up criteria for
analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results …

We consider the quasilinear parabolic–parabolic Keller–Segel system under homogeneous
Neumann boundary conditions in a convex smooth bounded domain Ω⊂ Rn with n⩾ 1. It is …

We determine the critical blow-up exponent for a Keller–Segel-type chemotaxis model,
where the chemotactic sensitivity equals some nonlinear function of the particle density …

The Keller-Segel system describes the collective motion of cells which are attracted by a
chemical substance and are able to emit it. In its simplest form it is a conservative drift …

In this paper, we use the diffusion-limit expansion of transport equations developed earlier
[T. Hillen and HG Othmer, SIAM J. Appl. Math., 61 (2000), pp. 751--775] to study the limiting …

The ability to invade tissue is one of the hallmarks of cancer. Cancer cells achieve this
through the secretion of matrix degrading enzymes, cell proliferation, loss of cell–cell …

Abstract The parabolic-parabolic Keller-Segel system for chemotaxis phenomena,(ut=∇·(φ
(u)∇ u)−∇·(ψ (u)∇ v), x∈ Ω, t> 0, vt=∆ v− v+ u, x∈ Ω, t> 0, is considered under …

We study a system arising in the modelling of the motion of swimming bacteria under the
effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty …