  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 positivity
and conditional global existence and uniqueness of the classical solutions of
the problem for large initial data.
