Global dynamics in a fully parabolic chemotaxis system with logistic source

Global Solutions for a Hyperbolic-parabolic System of Chemotaxis

We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.

Global existence of classical solutions to a combined chemotaxis–haptotaxis model with logistic source

a r t i c l e i n f o a b s t r a c t This paper deals with a mathematical model of cancer invasion of tissue. The model consists of a system of reaction–diffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. In two space dimensions, we prove global existence and uniqueness of classical solutions to this model ...

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 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...

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion