Singular limits arising in mechanical models of tissue growth
Singular limits arising in mechanical models of tissue growth
Based on the mechanical viewpoint that living tissues present a fluid-like behaviour, Partial Differential Equations models inspired by fluid dynamics are nowadays well established as one of the main mathematical tools for the macroscopic description of tissue growth. Depending on the type of tissue, these models link the pressure to the velocity field using either Brinkman’s law (visco-elastic models) or Darcy’s law (porous-medium equations (PME)).