Mathematical Analysis of a Kinetic Model for Cell Movement in Network Tissues

Details Mathematical Analysis of a Kinetic Model for Cell Movement in Network Tissues Mathematical Analysis of a Kinetic Model for Cell Movement in Network Tissues

2008-07-14

arxiv.org/abs/0807.2249v3

Discr. Contin. Dyn. Sys. B 14:1055-1080 (2010)

Mathematics

Analysis of PDEs

26 pages, 4 figures, revised and expanded version; to appear in Discr. Contin. Dyn. Sys. Ser. B

Scientific paper

Mesenchymal motion describes the movement of cells in biological tissues formed by fiber networks. An important example is the migration of tumor cells through collagen networks during the process of metastasis formation. We investigate the mesenchymal motion model proposed by T. Hillen (J. Math. Biol. 53:585-616, 2006) in higher dimensions. We formulate the problem as an evolution equation in a Banach space of measure-valued functions and use methods from semigroup theory to show the global existence of classical solutions. We investigate steady states of the model and show that patterns of network type exist as steady states. For the case of constant fiber distribution, we find an explicit solution and we prove the convergence to the parabolic limit.

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