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Garcke, Harald ; Lam, Kei Fong ; Sitka, Emanuel ; Styles, Vanessa

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.



Involved Institutions


Details

Item typeMonograph (Working Paper)
Series of the University of Regensburg:Preprintreihe der Fakultät Mathematik
Volume:15/2015
Date2015
InstitutionsMathematics > Prof. Dr. Harald Garcke
Identification Number
ValueType
1508.00437arXiv ID
Dewey Decimal Classification500 Science > 510 Mathematics
StatusUnknown
RefereedNo, this version has not been refereed yet (as with preprints)
Created at the University of RegensburgYes
URN of the UB Regensburgurn:nbn:de:bvb:355-epub-331291
Item ID33129

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