Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

A Quasi-linear Parabolic System of Chemotaxis

We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n-dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A(u), and that the diffusion coefficient of v is a positive constant. If A(u) is a positive constant, the system is referred to as socalled Keller-Segel system. In the case where th...

Boundedness in a Three-dimensional Attraction-repulsion Chemotaxis System with Nonlinear Diffusion and Logistic Source

This article concerns the attraction-repulsion chemotaxis system with nonlinear diffusion and logistic source, ut = ∇ · ((u+ 1)m−1∇u)−∇ · (χu∇v) +∇ · (ξu∇w) + ru− μu , x ∈ Ω, t > 0, vt = ∆v + αu− βv, x ∈ Ω, t > 0, wt = ∆w + γu− δw, x ∈ Ω, t > 0 under Neumann boundary conditions in a bounded domain Ω ⊂ R3 with smooth boundary. We show that if the diffusion is strong enough or the logistic dampen...

A priori bounds and global existence for a strongly coupled quasilinear parabolic system modeling chemotaxis

A priori bounds are found for solutions to a strongly coupled reactiondiffusion system that models competition of species in the presence of chemotaxis. These bounds are used to prove the existence of global solutions.

A Quasilinear Parabolic System with Nonlocal Boundary Condition

We investigate the blow-up properties of the positive solutions to a quasilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blow-up rate estimate. These extend the resent results of Wang et al. 2009 , which considered the spec...