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On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis

Volume 193 / 2009

Piotr Biler, Lorenzo Brandolese Studia Mathematica 193 (2009), 241-261 MSC: 35K57, 35B40. DOI: 10.4064/sm193-3-2

Abstract

We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller–Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.

Authors

  • Piotr BilerInstytut Matematyczny
    Uniwersytet Wroc/lawski
    pl. Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail
  • Lorenzo BrandoleseUniversité de Lyon
    Université Lyon 1
    Institut Camille Jordan, CNRS UMR 5208
    43 bd. du 11 Novembre
    69622 Villeurbanne Cedex, France
    e-mail

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