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Browsing by Author "Dawidowicz, Antoni Leon"

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    Item type:Article, Access status: Open Access ,
    On periodic and stable solutions of the Lasota equation in different phase spaces
    (2008) Dawidowicz, Antoni Leon; Poskrobko, Anna
    We study properties of the Lasota partial differential equation in two different spaces: $V_{\alpha}$ (Hölder continuous functions) and $L^{p}$. The aim of this paper is to generalize the results of [Z. Brzeźniak, A. L. Dawidowicz, <i>On the periodic solution to the von Foerster-Lasota equation</i>, to appear in Semigroup Forum].
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On the approximation theorem of Wong-Zakai type for the Lasota operator
    (2010) Dawidowicz, Antoni Leon; Twardowska, Krystyna
    We consider in this paper a stochastic evolution equation with Professor A. Lasota's operator as the infinitesimal generator of a strongly continuous semigroup of transformations and with Hammerstein operator connected with a noise being the Wiener process. We show that such evolution equation satisfies the Wong-Zakai type approximation theorem. The idea of the definition of the Lasota operator has the origin in the mathematical model of the creation and differentiation of cells in biology and medicine.