A density-dependent chemotaxis–haptotaxis system modeling cancer invasion

This paper deals with a chemotaxis–haptotaxis model of cancer invasion of tissue, initially proposed by Chaplain and Lolas. The model consists of three reaction–diffusion–taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. The equation for cell density includes two bounded nonlinear density-dependent chemotactic and haptotactic sensitivity functions. In the presence of logistic damping, we prove the global existence of a unique classical solution to this model by some delicate a priori estimate techniques.