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We consider a haptotaxis cancer invasion model that includes two families ofcancer cells. Both families, migrate on the extracellular matrix andproliferate. Moreover the model describes an epithelial-to-mesenchymal-liketransition between the two families, as well as a degradation and aself-reconstruction process of the extracellular matrix. We prove positivityand conditional global existence and uniqueness of the classical solutions ofthe problem for large initial data.

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