Global existence and large time behavior of solutions to a haptotaxis model with self-remodeling mechanisms

Abstract

In this paper, we deal with the initial-boundary value problem for the followinghaptotaxis model with self-remodeling mechanisms:beginalign*begincasesu_t=Δ u-ξ∇·(u∇ ω),v_t=Δ v-v+u,ωt=-vω+ηω(1-u-ω)endcasesendalign*in a bounded domain of $\\mathbb~R^2$ with zero-flux boundary conditions.We show that for any $\\eta>~0$, there existsa unique global classical solution. In particular, we show that the solution isuniformly bounded when $\\eta$ is appropriately small. On the basis of this, we also establish theglobal asymptotic stability of the constant steady state $(\\overline~u_0,~\\overline~u_0,~0)$.