Boundedness in a flux-limited chemotaxis-haptotaxis model with nonlinear diffusion

Boundedness in a chemotaxis–haptotaxis model with nonlinear diffusion

A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source

This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue (extracellular matrix, ECM). The model consists of a parabolic chemotaxis-haptotaxis PDE describing the evolution of cancer cell density, a parabolic PDE governing the evolution of matrix degrading enzyme concentration, and an ordinary differential equation reflecting the degradation of ECM. Following a recent appr...

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...

Chemotaxis and Haptotaxis on Cellular Level

Chemotaxis and haptotaxis have been a main theme in the macroscopic study of bacterial and cellular motility. In this work we investigate the influence these processes have on the shape and motility of fast migrating cells. We note that despite their biological and modelling differences, the cells exhibit many similarities in their migration. We moreover see, that after an initial adjustment ph...

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 ...