Yazar "Ismailov, Mansur I." seçeneğine göre listele

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    Existence and uniqueness of an inverse problem for nonlinear Klein-Gordon equation
    (Wiley, 2019) Tekin, İbrahim; Mehraliyev, Yashar T.; Ismailov, Mansur I.
    In this paper, an initial boundary value problem for nonlinear Klein-Gordon equation is considered. Giving an additional condition, a time-dependent coefficient multiplying nonlinear term is determined, and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem.
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    An inverse problem for finding the lowest term of a heat equation with Wentzell-Neumann boundary condition
    (Taylor & Francis Ltd, 2019) Ismailov, Mansur I.; Tekin, İbrahim; Erkovan, Sait
    tThe Fourier series analysis of the inverse problem of finding the coefficient of lowest term in the heat equation with a non-local Wentzell-Neumann boundary and integral overdetermination conditions is presented. Under some regularity, consistency and orthogonality conditions on the data and additional conditions on the sign of the Fourier coefficients of the initial data and known part of source term, the existence and uniqueness of the classical solution are shown by using the generalized Fourier method. Numerical solutions of the inverse problem are given both on a uniform grid and on a non-uniform grid with uniform finite difference method combined with the composite trapezoidal rule and with non-uniform finite difference method combined with Gauss-Lobatto quadrature, respectively. Two numerical examples (one is smooth while the other is non-smooth) will be provided to investigate the efficiency and the stability of the methods with respect to the coefficient of diffusive transport to the boundary.
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    Inverse scattering problem for linear system of four-wave interaction problem with equal number of incident and scattered waves
    (Birkhauser, 2021) Ismailov, Mansur I.; Tekin, İbrahim
    The first order semi-strict hyperbolic system on the semi-axis in the case of equal number of incident and scattered waves are considered. The uniqueness of the inverse scattering problem (the problem of finding the potential with respect to scattering operator) is studied by utilizing it to Gelfand–Levitan–Marchenko type linear integral equations. It is determined the sufficient quantity of scattering problems (on the semi-axis for the same hyperbolic system) for ensuring the uniqueness of the inverse scattering problem.