Dynamics of wavefronts to a coarse-grained model with volume-filling cell invasion

In this paper, we study stability of the traveling waves, obtained by Crossley et al. in 2023, to a coarse–grained model with small extracellular matrix degradation rate in the slow-fast setting. Since the information provided in the original proof is not enough to investigate stability, we present a new approach via geometric singular perturbation theory, which exhibits not only the structure but also an asymptotic expression of the waves. Then we show that the waves are spectrally instable in the Banach space formed by the bounded and uniformly continuous functions, and that the waves are spectrally stable in some exponential weight space.