Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis |
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Authors: | Matthias Ebenbeck Harald Garcke |
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Institution: | Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany |
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Abstract: | 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. |
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Keywords: | 35K35 35Q92 92C50 35D30 76D07 Tumour growth Cahn–Hilliard equation Brinkman's law Chemotaxis Stokes flow Outflow conditions |
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