Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms

We investigate a multiphase Cahn–Hilliard model for tumor growth with general source terms. The approach allows us to consider multiple cell types and chemical species (oxygen and/or nutrients) that are consumed by the tumor. Compared classical two-phase models, can be used describe stratified exhibiting several layers of tissue (e.g., proliferating, quiescent necrotic tissue) more precisely. Our consists convective type equation evolution, velocity associated volume-averaged field, reaction-diffusion density species. is either represented Darcy’s law or Brinkman equation. first construct global weak solution Cahn–Hilliard–Brinkman model. After that, we show such solutions this system converge Cahn–Hilliard–Darcy as viscosities tend zero in some suitable sense. This means existence also established.