@article{Huntul2024, 
author = {M. J. Huntul and Kh. Khompysh and M. K. Shazyndayeva and M. K. Iqbal},
title = {An inverse source problem for a pseudoparabolic equation with memory},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {14186-14212},
keywords = {inverse problem, pseudoparabolic equation, memory term, Tikhonov regularization, stability analysis, nonlinear optimization},
url = {https://www.sciopen.com/article/10.3934/math.2024689},
doi = {10.3934/math.2024689},
abstract = {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.}
}