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Inverse Problem of Finding the Coefficient of the Lowest Term in Two-Dimensional Heat Equation with Ionkin-Type Boundary Condition

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Abstract

We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin boundary and total energy integral overdetermination condition. The global well-posedness of the problem is obtained by generalized Fourier method combined with the unique solvability of the second kind Volterra integral equation. For obtaining a numerical solution of the inverse problem, we propose the discretization method from a new combination. On the one hand, it is known the traditional method of uniform finite difference combined with numerical integration on a uniform grid (trapezoidal and Simpson’s), on the other hand, we give the method of non-uniform finite difference is combined by a numerical integration on a non-uniform grid (with Gauss–Lobatto nodes). Numerical examples illustrate how to implement the method.

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Authors and Affiliations

  1. Gebze Technical University, Department of Mathematics, 41400, Gebze/Kocaeli, Turkey

    M. I. Ismailov & S. Erkovan

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, AZ1141, Baku, Azerbaijan

    M. I. Ismailov

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  1. M. I. Ismailov
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  2. S. Erkovan
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Correspondence to M. I. Ismailov or S. Erkovan.

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Ismailov, M.I., Erkovan, S. Inverse Problem of Finding the Coefficient of the Lowest Term in Two-Dimensional Heat Equation with Ionkin-Type Boundary Condition. Comput. Math. and Math. Phys. 59, 791–808 (2019). https://doi.org/10.1134/S0965542519050087

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