Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model


We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix.We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

Discrete Contin. Dyn. Syst. Ser. B