An inverse source problem for a pseudoparabolic equation with memory
Huntul M.J. Khompysh K. Shazyndayeva M.K. Iqbal M.K.
2024American Institute of Mathematical Sciences
AIMS Mathematics
2024#9Issue 614186 - 14212 pp.
This paper is devoted to investigating the well-posedness, as well as performing the numerical analysis, of an inverse source problem for linear pseudoparabolic equations with a memory term. The investigated inverse problem involves determining a right-hand side that depends on the spatial variable under the given observation at a final time along with the solution function. Under suitable assumptions on the problem data, the existence, uniqueness and stability of a strong generalized solution of the studied inverse problem are obtained. In addition, the pseudoparabolic problem is discretized using extended cubic B-spline functions and recast as a nonlinear least-squares minimization of the Tikhonov regularization function. Numerically, this problem is effectively solved using the MATLAB subroutine lsqnonlin. Both exact and noisy data are inverted. Numerical results for a benchmark test example are presented and discussed. Moreover, the von Neumann stability analysis is also discussed.
inverse problem , memory term , nonlinear optimization , pseudoparabolic equation , stability analysis , Tikhonov regularization
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Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan, 45142, Saudi Arabia
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics, Government College University, Faisalabad, Pakistan
Department of Mathematics
Al-Farabi Kazakh National University
Department of Mathematics
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