This paper proposes a survey and critical analysis focused on a variety of chemotaxis
models in biology, namely the classical Keller–Segel model and its subsequent …

In 1970 Keller and Segel [15] proposed a mathematical model describing chemotactic
aggregation of cellular slime molds which move preferentially towards relatively high …

In this paper, we study the long time behavior of a one-dimensional reaction diffusion system
appearing in mathematical biology by using the theory of infinite dimensional dynamical …

Abstract We consider the Nernst–Planck–Navier–Stokes system in a bounded domain of R
d, d= 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic …

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Existence of local and global in time solutions for parabolic-elliptic and parabolic systems
describing the aggregation of the cellular slime mould by the chemical attraction is studied …

This paper deals with the coupled chemotaxis–haptotaxis model {ut= Δ u− χ∇⋅(u∇ v)−
ξ∇⋅(u∇ w)+ μ u (1− u− w), x∈ Ω, t> 0, 0= Δ v+ u− v, x∈ Ω, t> 0, wt=− v w+ η w (1− w− u) …

We carry on our studies related to the fully parabolic quasilinear Keller–Segel system started
in [6] and continued in [7]. In the above mentioned papers we proved finite-time blowup of …

This work considers the Keller–Segel-type parabolic system ut= Δ (u ϕ (v)), x∈ Ω, t> 0,<?
A3B2 [rowsep= 4pt]?> vt= Δ v− v+ u, x∈ Ω, t> 0,(⋆) in a smoothly bounded convex domain …

This chapter returns to the general W (x) and describes the fact that the varia-tional structure
F defined on Pλ and that of Jλ on V= dom (A 1/2) stated in Chapter 6 are equivalent up to …