  This work studies the chemotaxis-haptotaxis system
  $$\left\{ \begin{array}{ll} u_t= \Delta u - \chi \nabla \cdot (u\nabla v) -
\xi \nabla \cdot (u\nabla w) + \mu u(1-u-w), &\qquad x\in \Omega, \, t>0,
\\[1mm]
  v_t=\Delta v-v+u, &\qquad x\in \Omega, \, t>0, \\[1mm]
  w_t=-vw, &\qquad x\in \Omega, \, t>0, \end{array} \right. $$
  in a bounded smooth domain $\Omega\subset\mathbb{R}^2$ with zero-flux
boundary conditions, where the parameters $\chi, \xi$ and $\mu$ are assumed to
be positive. It is shown that under appropriate regularity assumption on the
initial data $(u_0, v_0, w_0)$, the corresponding initial-boundary problem
possesses a unique classical solution which is global in time and bounded. In
addition to coupled estimate techniques, a novel ingredient in the proof is to
establish a one-sided pointwise estimate, which connects $\Delta w$ to $v$ and
thereby enables us to derive useful energy-type inequalities that bypass $w$.
However, we note that the approach developed in this paper seems to be confined
to the two-dimensional setting.
