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Stationary solutions of aerotaxis equations

Volume 42 / 2015

Piotr Knosalla, Tadeusz Nadzieja Applicationes Mathematicae 42 (2015), 125-135 MSC: Primary 35J66; Secondary 92C45. DOI: 10.4064/am42-2-1

Abstract

We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these parameters and the maximum of the energy function.

Authors

  • Piotr KnosallaInstitute of Mathematics and Informatics
    Opole University
    Oleska 48
    45-052 Opole, Poland
    e-mail
  • Tadeusz NadziejaInstitute of Mathematics and Informatics
    Opole University
    Oleska 48
    45-052 Opole, Poland
    e-mail

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