Global existence and boundedness in a chemotaxis-convection model with sensitivity functions for tumor angiogenesis

Abstract

This paper deals with the fully parabolic chemotaxis-convection model with sensitivity functions for tumor angiogenesis, \begin{align*} \begin{cases} u_t=Δu-\nabla \cdot (uχ_1(v)\nabla v) +\nabla \cdot (uχ_2(w)\nabla w), &x \in Ω,\ t>0, \\[1.05mm] v_t=Δv+\nabla \cdot (vξ(w)\nabla w)+αu-βv, &x \in Ω,\ t>0, \\[1.05mm] w_t=Δw+γu-δw, &x \in Ω,\ t>0 \end{cases} \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $\Omega \subset {\mathbb{R}}^n$ $(n\le 3)$ is a bounded domain with smooth boundary, ${\chi }_1,{\chi }_2,\xi$ are functions satisfying some conditions and $\alpha ,\beta ,\gamma ,\delta >0$ are constants. The purpose of this paper is to establish global existence and boundedness in this system.