An inverse problem for pseudoparabolic equation: existence, uniqueness, stability, and numerical analysis
Khompysh K. Huntul M.J. Shazyndayeva M.K. Iqbal M.K.
2024Taylor and Francis Ltd.
Quaestiones Mathematicae
2024#47Issue 101979 - 2001 pp.
In this paper, we study an inverse problem for a linear third-order pseudoparabolic equation. The investigated inverse problem consists of determining a space-dependent coefficient of the right-hand side of a pseudoparabolic equation. As an additional information a final overdetermination condition is considered. Under the suitable conditions on the data of the problem, the unique solvability of the considered inverse problem is established. The stability of solutions is also proved. The established results are also true for inverse problems for parabolic equations, which could be obtained as a regularization of the studied pseudoparabolic equation. In addition, the pseudoparabolic problem is discretized using the cubic B-spline functions and recast as a nonlinear least-squares minimization of the Tikhonov regularization function. Numerically, this is effectively solved using the MATLAB subroutine lsqnonlin. Both exact and noisy data are inverted. Numerical results for three benchmark test examples are presented and discussed. Moreover, the von Neumann stability analysis is also discussed.
Inverse problem , nonlinear optimization , pseudoparabolic equation , stability analysis , Tikhonov regularization
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia
Al-Farabi Kazakh National University, E-Mail, Almaty, Kazakhstan
Department of Mathematics, Government College University, Faisalabad, Pakistan
Al-Farabi Kazakh National University
Department of Mathematics
Al-Farabi Kazakh National University
Department of Mathematics
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