Global boundedness of classical solutions to a two species cancer invasion haptotaxis model with tissue remodeling

Abstract

In this paper, we deal with a haptotaxis cancer invasion model describing the migration and proliferation of two families of cancer cells, the epithelial-mesenchymal transition between two families cancer cells, the dynamics of matrix degrading enzymes, and the evolution and re-modeling of the extracellular matrix. Under appropriate regularity assumptions on initial data, by making some a priori estimates and applying iterative techniques, we establish the global existence and uniform boundedness of the unique classical solution in two-dimensional spatial domain for arbitrary cancer cells proliferation rates and in three-dimensional spatial setting for large cancer cells proliferation rates. These results improve and extend previously known ones.