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Sergei Trofimchuk

  1. Positive travelling fronts for reaction-diffusion systems with distributed delay.

    Tue, 05/18/2010 - 15:01 — SomNambul
    Authors: Sergei Trofimchuk, Teresa Faria
    Subjects: Classical Analysis and ODEs
    Abstract

    We give sufficient conditions for the existence of positive travelling wave
    solutions for multi-dimensional autonomous reaction-diffusion systems with
    distributed delay. To prove the existence of travelling waves, we give an
    abstract formulation of the equation for the wave profiles in some suitable
    Banach spaces, and apply known results about the index of some associated
    Fredholm operators.

  2. Monotone traveling wavefronts of the KPP-Fisher delayed equation.

    Thu, 01/21/2010 - 16:01 — SomNambul
    Authors: Adrian Gomez, Sergei Trofimchuk
    Subjects: Classical Analysis and ODEs
    Abstract

    In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002)
    initiated the study of the positive wavefronts in the delayed
    Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has
    become one of the most popular objects in the studies of traveling waves for
    the monostable delayed reaction-diffusion equations. In this paper, we give a
    complete solution to the problem of existence and uniqueness of monotone waves
    in the KPP-Fisher equation. We show that each monotone traveling wave can be
    found via an iteration procedure.

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