Geodesic
Free boundary problems for Stokes flow, with applications to the growth of biological tissues
John R. King1 ; Chandrasekhar Venkataraman2
1The University of Nottingham, UK
2University of Sussex, Brighton, UK
Interfaces and free boundaries, Tome 23 (2021) no. 4, pp. 433-458

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DOI

We formulate, analyse and numerically simulate what are arguably the two simplest Stokes-flow free boundary problems relevant to tissue growth, extending the classical Stokes free boundary problem by incorporating (i) a volumetric source (the nutrient-rich case) and (ii) a volumetric sink, a surface source and surface compression (the nutrient-poor case). Both two- and three-dimensional cases are considered. A number of phenomena are identified and characterised thereby, most notably a buckling-associated instability in case (ii).
DOI : 10.4171/ifb/459
Classification : 35-XX, 76-XX
Mots-clés : Stokes-flow, tissue growth, moving boundary problems, finite element methods

John R. King  1   ; Chandrasekhar Venkataraman  2

1 The University of Nottingham, UK
2 University of Sussex, Brighton, UK 
John R. King; Chandrasekhar Venkataraman. Free boundary problems for Stokes flow, with applications to the growth of biological tissues. Interfaces and free boundaries, Tome 23 (2021) no. 4, pp. 433-458. doi: 10.4171/ifb/459
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     year = {2021},
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