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 this paper, we study nonnegative and classical solutions u= u (x, t) u= u (x, t) to porous
medium problems of the type where Ω Ω is a bounded and smooth domain of R^ N RN, with …

This paper deals with a nonlinear system of two partial differential equations arising in
chemotaxis, involving a source term of logistic type. The existence of global bounded …

We prove existence of global weak solutions to the chemotaxis system ut= Δ u−∇⋅(u∇ v)+
κ u− μ u 2 vt= Δ v− v+ u under homogeneous Neumann boundary conditions in a smooth …

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for
attracting microbes to food, embryonic cells into developing tissues, immune cells to …

We consider nonnegative solutions of the Neumann initial-boundary value problem for the
chemotaxis-growth system {u_t= ε u_ xx-(uv_x) _x+ ru-μ u^ 2,\qquad x ∈ Ω,\t> 0,\0= v_ xx-v+ …

In this paper we explore the dynamics of a one-dimensional Keller–Segel type model for
chemotaxis incorporating a logistic cell growth term. We demonstrate the capacity of the …

The ability of cancer cells to break out of tissue compartments and invade locally gives solid
tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling …

In this paper, we are concerned with a general class of quasilinear parabolic–parabolic
chemotaxis systems with/without growth source, under homogeneous Neumann boundary …

In this article we investigate a parabolic–parabolic-elliptic two-species chemotaxis system
with weak competition and show global asymptotic stability of the coexistence steady state …