Abstract: "Based on the mechanical perspective that living tissues exhibit fluid-like behavior, PDE models inspired by fluid dynamics are increasingly applied to describe tissue growth at the macroscopic level. These models link the pressure to the velocity field depending on the type of tissue, using either Brinkman’s law (viscoelastic models) or Darcy’s law (porous-medium equation, PME). The stiffness of the pressure law plays a crucial role in distinguishing between compressible (density-based) models and incompressible (free boundary) problems, where density saturation occurs. In this talk, I will explore how different mechanical models of living tissues can be related through singular limits. Specifically, I will discuss the inviscid limit leading to the PME and the incompressible limit from the PME to Hele-Shaw free boundary problems. Furthermore, I will present a recent result on their joint limit, which is derived using energy dissipation inequalities, a method reminiscent of the EDI characterization for gradient flows."