Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
