Global existence for a haptotaxis model of cancer invasion with tissue remodeling

This paper considers a 3×3 haptotaxis model of cancer invasion with tissue remodeling. The model consists of a parabolic haptotaxis partial differential equation (PDE) describing the evolution of tumor cell density, an ordinary differential equation modeling the proteolysis and the remodeling of the extracellular matrix (ECM), and a parabolic PDE governing the evolution of the matrix degrading enzyme (MDE) concentration. In addition to random diffusion, tumor cells are biased towards higher ECM density, which is referred to as haptotaxis. Under a restrictive assumption on the coefficients, the global existence and uniqueness of classical solutions to the model in two dimensions, along with the boundedness of solutions in two and three dimensions, is proved by establishing some delicate a priori estimates.