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    Wyświetlanie 1-4 z 4
    Tytuł:
    Construction of integral equations describing limit equilibrium of cylindrical shell with a longitudinal crack under time-varying load
    Autorzy:
    Makhorkin, M.
    Nykolyshyn, M
    Powiązania:
    https://bibliotekanauki.pl/articles/411396.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    cylindrical shell
    crack
    exponential time dependence
    varying load
    system of singular integral equations
    Opis:
    The problem on limit equilibrium of a closed infinite cylindrical shell with a longitudinal crack under the action of time-varying load by the exponential law has been considered. According to presented conditions the expressions for the field of the stress-free deformations along the crack are presented in the form [wzory] are the operators identical to those given in [7] for the case of static load [wzory] and , are the operators that take into account the dependence of load on time. Using the same transformations that in the case of static load [7, 11], the key functions [wzory] are determined, and the clarification of the shell's stress-state is reduced to solving the system of singular integral equations (SIE). Its general form is similar to the same system constructed for static load [7], and the kernels of SIE have the form [wzory], where is a singular part [wzory], is a regular part in which the component [wzory] takes into account the time dependence of load [wzory], are described by the expressions similar to the same given in [7].
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 3; 141-146
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the number of positive solutions to a class of integral equations
    Autorzy:
    Wang, L.
    Yu, W.
    Zhang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/206271.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie całkowe
    rozwiązanie dodatnie
    integral equations
    positive solutions
    complete discrimination system for polynomials
    number of solutions
    Opis:
    By using the complete discrimination system for polynomials, we study the number of positive solutions in C[0,1] to the integral equation phi(x) = integral[...] k(x,y)phi^n(y)dy, where k(x,y) = phi1(x)phi1(y)+phi2(x)phi2(y),[phi]i(x) > 0,[phi]i(y) > 0,0 < x,y < 1,i = 1,2, are continuous functions on [0,1], n is a positive integer. We prove the following results: when n = 1, either there does not exist, or there exist infinitely many positive solutions in C[0,1]; when n [is greater than or equal] 2, there exist at least 1, at most n + 1 positive solutions in C[0,1]. Necessary and sufficient conditions are derived for the cases: 1) n = 1, there exist positive solutions; 2) n [is greater than or equal to] 2, there exist exactly m (m belongs to {1,2,..., n + 1}) positive solutions. Our results generalize the ones existing in the literature, and their usefulness is shown by examples.
    Źródło:
    Control and Cybernetics; 2003, 32, 2; 383-395
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pseudo-differential equations and conical potentials: 2-dimensional case
    Autorzy:
    Vasilyev, Vladimir B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255700.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    pseudo-differential equation
    wave factorization
    Dirichlet problem
    system of linear integral equations
    Opis:
    We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 109-124
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solving linear Fredholm integro-differential equation by Nyström method
    Autorzy:
    Tair, Boutheina
    Guebbai, Hamza
    Segni, Sami
    Ghiat, Mourad
    Powiązania:
    https://bibliotekanauki.pl/articles/1839836.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Fredholm integral equation
    system of integral equations
    integro-differential equations
    Nyström method
    równanie całkowe Fredholma
    układ równań całkowych
    równanie całkowo-różniczkowe
    metoda Nyströma
    Opis:
    The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nyström method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C1 [a,b]. We have applied the Nystrom method based on the trapezoidal ¨ rule to avoid adding other conditions in order to the approximation method’s convergence. The Nyström method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nyström method, some numerical examples will be provided at the end of this work.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 3; 53-64
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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