  In this paper, we carry out a travelling-wave analysis of a model of tumour
invasion with degenerate, cross-dependent diffusion. We consider two types of
invasive fronts of tumour tissue into extracellular matrix (ECM), which
represents healthy tissue. These types differ according to whether the density
of ECM far ahead of the wave front is maximal or not. In the former case, we
use a shooting argument to prove that there exists a unique travelling wave
solution for any positive propagation speed. In the latter case, we further
develop this argument to prove that there exists a unique travelling wave
solution for any propagation speed greater than or equal to a strictly positive
minimal wave speed. Using a combination of analytical and numerical results, we
conjecture that the minimal wave speed depends monotonically on the degradation
rate of ECM by tumour cells and the ECM density far ahead of the front.
