  Phase field models recently gained a lot of interest in the context of tumour
growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard
equations. However, often Stokes or Brinkman flows are more appropriate flow
models. We introduce and mathematically analyse a new Cahn-Hilliard-Brinkman
model for tumour growth allowing for chemotaxis. Outflow boundary conditions
are considered in order not to influence tumour growth by artificial boundary
conditions. Existence of global-in-time weak solutions is shown in a very
general setting.
