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This paper deals with the Neumann problem for the coupled quasilinear chemotaxis-haptotaxis model of cancer invasion given by \begin{document}$\left\{ \begin{gathered} ut = \nabla \cdot \left( {{{\left( {u + 1} \right)}^{m - 1}}\nabla u} \right) - \nabla \cdot \left( {u\nabla v} \right) - \nabla \cdot \left( {u\nabla w} \right) + u\left( {1 - u - w} \right), \hfill \\ ut = \Delta v - v + u, \hfill \\ wt = - vw, \hfill \\ \end{gathered} \right.$ \end{document} where the parameter $m≥q1$ and $\mathbb{R}^N(N≥q2)$ is a bounded domain with smooth boundary. If $m>\frac{2N}{N+2}$, then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded. The results of this paper partly extend previous results of several authors.

Boundedness of solutions to a quasilinear higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion