A multiphase Cahn--Hilliard--Darcy model for tumour growth with necrosis

@article{Garcke2017AMC,
  title={A multiphase Cahn--Hilliard--Darcy model for tumour growth with necrosis},
  author={Harald Garcke and Kei Fong Lam and Robert Nurnberg and Emanuel Sitka},
  journal={Mathematical Models and Methods in Applied Sciences},
  year={2017},
  volume={28},
  pages={525-577}
}
We derive a Cahn–Hilliard–Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. A multitude of phenomena such as nutrient diffusion and consumption, angiogenesis, hypoxia, blood vessel growth, and inhibition by toxic agents, which are released for example by the necrotic cells, are included. A new feature of the modelling approach is that a volume… 
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