Yazar "Ismailov, M. I." seçeneğine göre listele

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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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    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.