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=\Delta u-\nabla \cdot (u\chi_1(v)\nabla v) +\nabla \cdot (u\chi_2(w)\nabla w), &x \in \Omega,\ t>0, \\[1.05mm] v_t=\Delta v+\nabla \cdot (v\xi(w)\nabla w)+\alpha u-\beta v, &x \in \Omega,\ t>0, \\[1.05mm] w_t=\Delta w+\gamma u-\delta w, &x \in \Omega,\ 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.