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Browsing by Subject "cone"

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  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Istnienie rozwiązań dodatnich dla pewnej klasy problemów brzegowych
    (Data obrony: 2009-07-08) Goncerz, Paweł
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Positive solutions to a third order nonlocal boundary value problem with a parameter
    (Wydawnictwa AGH, 2024) Szajnowska, Gabriela; Zima, Mirosława
    We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel'skiĭ-Guo fixed point theorem in cones and the properties of the Green's function corresponding to the BVP under study. The main results are illustrated by suitable examples.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Solution of the boundary value problem of heat conduction in a cone
    (Wydawnictwa AGH, 2022) Ramazanov, Murat; Dženaliev, Muvašarhan Tanabievič; Gulmanov, Nurtay
    In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable. In practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman-Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.