IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-55627-2_22.html

Nonlinear Hyperbolic Systems of Generalized Navier-Stokes Type for Interactive Motion in Biology

In: Geometric Analysis and Nonlinear Partial Differential Equations

Author

Listed:
  • Wolfgang Alt

    (Universität Bonn, Abteilung Theoretische Biologie, Botanisches Institut)

Abstract

Summary We review two modelling approaches to obtain genuinely nonlinear systems of one hyperbolic transport equation (for density) accompanied by parabolic or elliptic equations (for mean velocity and, eventually, pressure), namely generalized Navier-Stokes or (pseudostationary) Stokes equations. Background and applications are related to models of interactive biological motion, namely for contractile polymer networks in intra-cellular motility, for cell movement and tissue formation during wound healing as well as for cohorts of migrating birds. One approach is to derive, after suitable scaling, a formal continuum limit of (stochastic) Hamiltonian equations for ‘visco-elastic’ multi-particle networks with specific interaction laws. The other consists in the derivation of (highly) viscous two-phase flow equations by minimization of a corresponding energy-loss functional. In both procedures there remain convergence or existence problems to be solved analytically. Some results and a few numerical simulations are shown, particularly for the 1-dimensional case. For further results, technical details and for comparison with other methods we give corresponding references.

Suggested Citation

  • Wolfgang Alt, 2003. "Nonlinear Hyperbolic Systems of Generalized Navier-Stokes Type for Interactive Motion in Biology," Springer Books, in: Stefan Hildebrandt & Hermann Karcher (ed.), Geometric Analysis and Nonlinear Partial Differential Equations, pages 431-461, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55627-2_22
    DOI: 10.1007/978-3-642-55627-2_22
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-55627-2_22. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.