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 …

The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of
tumor angiogenesis in two and three dimensional whole spaces is investigated in the paper …

The chemotaxis system {ut= Δ u−∇⋅(uv∇ v), vt= Δ v− uv,(⋆) is considered under
homogeneous Neumann boundary conditions in the ball Ω= BR (0)⊂ R n, where R> 0 and …

We consider the chemotaxis system ut= Δ u−∇⋅ uv∇ v,<? A3B2 [rowsep= 6pt]?> vt= Δ v−
uv, as originally introduced in 1971 by Keller and Segel in the second of their seminal works …

In this paper, we study the qualitative behavior of the Cauchy problem of a hyperbolic model
\left{p_t-∇⋅\left(pq\right)\,=\,Δp,\,x∈\CalR^d,t>0,\hfillq_t-∇\left(ε|q|^2+p\right)\,=\,εΔq,\hfill\cr …

This paper is devoted to the study of the existence and stability of non-trivial steady state
solutions to the following coupled system of PDEs on the half-line R+=(0,∞): ut= uxx− χ [u (ln …

The chemotaxis system {ut=∇⋅(D (u)∇ u)−∇⋅(u S (x, u, v)⋅∇ v), vt= Δ v− uv, is considered
in a bounded domain Ω⊂ R n, n≥ 2, with smooth boundary. It is shown that if …

We explore the existence and nonlinear stability of boundary spike‐layer solutions of the
Keller–Segel system with logarithmic singular sensitivity in the half space, where the …

This paper is concerned with the stability of boundary layer solutions for a viscous
hyperbolic system transformed via a Cole--Hopf transformation from a singular chemotactic …

We study the chemotaxis–fluid system {n t+ u⋅∇ n= Δ n−∇⋅(nc∇ c), x∈ Ω, t> 0, c t+ u⋅∇
c= Δ c− nc, x∈ Ω, t> 0, u t+∇ P= Δ u+ n∇ ϕ, x∈ Ω, t> 0,∇⋅ u= 0, x∈ Ω, t> 0, under …