Yazar "Tekin, İbrahim" seçeneğine göre listele

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    A New Approach for Unique Restoration of a Time-Dependent Matrix Potential in a Hyperbolic Scattering Problem on the Semi-Axis
    (Inst Math & Mechanics Azerbaijan, 2019) Ismailov, M. I.; Tekin, İbrahim
    This paper considers the inverse scattering problem on the semi-axis for the matrix hyperbolic system with a special structure of matrix potential. The possible relationship between the matrix scattering operators for the first order systems with unshifted and space-shifted potentials is given. By using this relationship, the new approach for unique restoration of this potential from the matrix scattering operators on the semi-axis is given.
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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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    An Inverse Problem for the Forced Transverse Vibration of a Rectangular Membrane with Time Dependent Potential
    (2020) Tekin, İbrahim
    In this paper, an initial-boundary value problem for a two-dimensional waveequation which arises in the equation of motion for the forced transverse vibration of a rectangular membrane is considered. Giving an additional condition, a time-dependentcoefficient is determined and existence anduniqueness theorem for smalltimes is proved.Moreover, characterization of the conditional stability isgivenand numerical solution of the inverse probleminvestigatedby using finite difference method.
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    Determination of a time-dependent coefficient in a non-linear hyperbolic equation with non-classical boundary condition
    (Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2021) Tekin, İbrahim
    The non-linear hyperbolic equation is used to model many non-linear phenomena. In this paper, we consider an initial boundary value problem for non-linear hyperbolic equation. We determine a time-dependent coefficient multiplying non-linear term by using an additional condition, and prove the existence and uniqueness theorem for small times. We also propose a numerical scheme to solve the inverse problem for non-linear hyperbolic equation, and give test examples for sine, quadratic and cubic non-linearity.
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    Determination of a Time-Dependent Coefficient in a Wave Equation with Unusual Boundary Condition
    (Univ Nis, Fac Sci Math, 2019) Tekin, İbrahim
    In this paper, an initial boundary value problem for a wave equation with unusual boundary condition is considered. Giving an integral over-determination condition, a time-dependent potential is determined and existence and uniqueness theorem for small times is proved. We characterize the estimates of conditional stability of the solution of the inverse problem. Also, the numerical solution of the inverse problem is studied by using finite difference method.
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    Determination of a time-dependent potential in a Rayleigh-Love equation with non-classical boundary condition
    (Ankara Üniversitesi, 2021) Tekin, İbrahim
    Mathematical model of the longitudinal vibration of bars includes higher-order derivatives in the equation of motion under considering the effect of the lateral motion of a relatively thick bar. This paper considers such an inverse coefficient problem of determining time-dependent potential of a linear source together with the unknown longitudinal displacement from a Rayleigh-Love equation (containing the fourth-order space derivative) by using an additional measurement. Existence and uniqueness theorem of the considered inverse coefficient problem is proved for small times by using contraction principle.
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    Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem
    (Taylor & Francis Ltd, 2019) Zhuo, L.; Lesnic, D.; Ismailov, M. I.; Tekin, İbrahim; Meng, S.
    Diffusion processes with reaction generated by a nonlinear source are commonly encountered in practical applications related to ignition, pyrolysis and polymerization. In such processes, determining the intensity of reaction in time is of crucial importance for control and monitoring purposes. Therefore, this paper is devoted to such an identification problem of determining the time-dependent coefficient of a nonlinear heat source together with the unknown heat flux at an inaccessible boundary of a one-dimensional slab from temperature measurements at two sensor locations in the context of nonlinear transient heat conduction. Local existence and uniqueness results for the inverse coefficient problem are proved when the first three derivatives of the nonlinear source term are Lipschitz continuous functions. Furthermore, the conjugate gradient method (CGM) for separately reconstructing the reaction coefficient and the heat flux is developed. The ill-posedness is overcome by using the discrepancy principle to stop the iteration procedure of CGM when the input data is contaminated with noise. Numerical results show that the inverse solutions are accurate and stable.
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    Existence and uniqueness of an inverse problem for a second order hyperbolic equation
    (Emrah Evren KARA, 2018) Tekin, İbrahim
    In this paper, an initial boundary value problem for a second order hyperbolic equation is considered. Giving an additional condition, a time-dependent coefficient multiplying a linear term is determined and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem numerically.
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    EXISTENCE AND UNIQUENESS OF AN INVERSE PROBLEM FOR A WAVE EQUATION WITH DYNAMIC BOUNDARY CONDITION
    (Turkic World Mathematical Soc, 2020) Tekin, İbrahim
    In this paper, an initial boundary value problem for a wave equation with dynamic boundary condition is considered. Giving an additional condition, a time-dependent coefficient is determined and existence and uniqueness theorem for small times is proved.
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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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    Inverse problem for the time-fractional euler-bernoulli beam equation
    (VGTU, 2021) Tekin, İbrahim; Yang, He
    In this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.
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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.
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    RECONSTRUCTION OF A TIME-DEPENDENT POTENTIAL IN A PSEUDO-HYPERBOLIC EQUATION
    (Univ Politehnica Bucharest, Sci Bull, 2019) Tekin, İbrahim
    In this paper, an initial boundary value problem for a pseudo-hyperbolic equation is considered. Giving an over-determination condition, a time-dependent potential is determined and existence and uniqueness theorem for small times is proved. Also, theorem of the conventional stability of the solution of the inverse problem is given.