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In recent years, there has been a spike in the interest in multi-phase tissuegrowth models. Depending on the type of tissue, the velocity is linked to thepressure through Stoke's law, Brinkman's law or Darcy's law. While each ofthese velocity-pressure relations has been studied in the literature, littleemphasis has been placed on the fine relationship between them. In this paper,we want to address this dearth in the literature, providing a rigorous argumentthat bridges the gap between a viscoelastic tumour model (of Brinkman type) andan inviscid tumour model (of Darcy type).

A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model