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A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport
Garcke, Harald, Lam, Kei Fong, Sitka, Emanuel and Styles, Vanessa (2015) A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Preprintreihe der Fakultät Mathematik 15/2015, Working Paper.Date of publication of this fulltext: 11 Jan 2016 13:45
Monograph
DOI to cite this document: 10.5283/epub.33129
Abstract
Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several ...
Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new active transport term is analysed. Numerical computations are performed to study the influence of the active transport term for specific growth scenarios.
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| Item type | Monograph (Working Paper) | ||||
| Series of the University of Regensburg: | Preprintreihe der Fakultät Mathematik | ||||
|---|---|---|---|---|---|
| Volume: | 15/2015 | ||||
| Date | 2015 | ||||
| Institutions | Mathematics > Prof. Dr. Harald Garcke | ||||
| Identification Number |
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| Dewey Decimal Classification | 500 Science > 510 Mathematics | ||||
| Status | Unknown | ||||
| Refereed | No, this version has not been refereed yet (as with preprints) | ||||
| Created at the University of Regensburg | Yes | ||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-331291 | ||||
| Item ID | 33129 |
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