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2010, Volume 14, Issue 3: 1055-1080. Doi: 10.3934/dcdsb.2010.14.1055
This issue Previous Article A spectral collocation method for solving initial value problems of first order ordinary differential equations Next Article Analysis of a predator-prey model with predators impulsively diffusing between two patches

Mathematical analysis of a kinetic model for cell movement in network tissues

  • 1.

    Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, Edmonton, T6G 2G1

  • 2.

    Department of Mathematical Sciences, University of Wisconsin – Milwaukee, P.O. Box 413, Milwaukee, WI 53201-0413

  • 3.

    Department of Mathematics, Vanderbilt University, Nashville, TN 37240

Received:  February 28, 2009
Revised:  February 28, 2010
Published:  September 2010
Abstract Related Papers Cited by
    Abstract
  • Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks. An important example is the migration of tumour cells through collagen networks during the process of metastasis formation. We investigate the mesenchymal motion model proposed by T. Hillen in [14] 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 mild and 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 fibre distribution, we find an explicit solution and we prove the convergence to the parabolic limit.
    Mathematics Subject Classification: Primary: 35L03; Secondary: 92C17.

    Citation:
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