Large time behavior of solution to a fully parabolic chemotaxis-haptotaxis model in higher dimensions

This paper deals with the chemotaxis-haptotaxis model of cancer invasion in a bounded smooth domain Ω⊂Rn with zero-flux boundary conditions, where χ, ξ and μ are positive parameters. It is shown that if μ/χ is suitably large then for all sufficiently smooth initial data, the associated initial-boundary-value problem possesses a unique global-in-time classical solution that is bounded in Ω×(0, ∞), and if the initial data w0 is small, w becomes asymptotically negligible. Moreover, we prove that when domain Ω is convex, (1μ,1μ,0) is globally asymptotically stable provided that u₀≢0 and thereby extends the result of Hillen et al. (2013) [18] to the higher space dimensions.