The no‐flux initial‐boundary value problem for the quasilinear Keller–Segel system*
ut=∇·(D (u)∇ u)−∇·(S (u)∇ v), vt= Δ v− v+ u,* 6pc\left {\def & is considered in smoothly …

Abstract The Keller-Segel-Navier-Stokes system {n t+ u⋅∇ n= Δ n−∇⋅(n χ (n)∇ c), c t+
u⋅∇ c= Δ c− c+ n, u t+(u⋅∇) u= Δ u+∇ P+ n∇ Φ,∇⋅ u= 0,(⋆) is considered in a smoothly …

Global existence and boundedness of solutions to the Cauchy problem for the four
dimensional fully parabolic chemotaxis system with indirect signal production are studied …

The Neumann problem for the Keller-Segel system $\left\{\begin {array}{l}
u_t=\nabla\cdot\left (D\left (u\right)\nabla u\right)-\nabla\cdot\left (S\left (u\right)\nabla …

Abstract The quasilinear Keller–Segel system ut=∇·(D (u)∇ u)-∇·(S (u)∇ v), vt= Δ v-v+ u,
endowed with homogeneous Neumann boundary conditions is considered in a bounded …

The paper should be viewed as complement of an earlier result in [8]. In the paper just
mentioned it is shown that 1d case of a quasilinear parabolic-elliptic Keller-Segel system is …

This note deals with a one-dimensional quasilinear chemotaxis system. The first part
summarizes recent results, in which a new energy-like functional is introduced and plays a …

In a ball Ω= BR (0)⊂ R n, n≥ 2, the chemotaxis system ut=∇·(D (u)∇ u)-∇·(u S (u)∇ v), 0=
Δ v-μ+ u, μ= 1| Ω|∫ Ω u,(⋆) is considered under no-flux boundary conditions, with a focus on …

It is known since 2010 (see Cieslak and Laurencot, DCDS 2010) that in a parabolic-elliptic
quasilinear Keller-Segel system critical nonlinear diffusion does not exist. Either all the …

Refined investigation of chemotaxis processes has revealed a significant role of
degeneracies in corresponding motilities in a number of application contexts. A rapidly …