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

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 59; no. 5; pp. 791 - 808
Main Authors: Ismailov, M. I., Erkovan, S.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.05.2019
Springer Nature B.V
Subjects:
Boundary conditions
Computational Mathematics and Numerical Analysis
Economic models
Finite difference method
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical integration
Thermodynamics
Time dependence
Volterra integral equations
Well posed problems
generalized Fourier method
non-uniform finite difference method
Ionkin-type boundary condition
numerical integration
2D heat equation
uniform finite difference method
Volterra integral equation
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary: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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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542519050087