Global existence versus blow up for some models of interacting particles

Volume 106 / 2006

Piotr Biler, Lorenzo Brandolese Colloquium Mathematicum 106 (2006), 293-303 MSC: 35K60, 35B40, 82C21. DOI: 10.4064/cm106-2-9

Abstract

We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst–Planck and Debye–Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.

Authors

  • Piotr BilerInstytut Matematyczny
    Uniwersytet Wroc/lawski
    Pl. Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail
  • Lorenzo BrandoleseInstitut Camille Jordan
    Université Claude Bernard-Lyon 1
    21 avenue Claude Bernard
    69622 Villeurbanne Cedex, France
    e-mail

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