Simultaneous identification of the solely time-dependent potential and source control terms from known moisture moments
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Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Wiley
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Pseudo-parabolic equations are commonly used as mathematical models in mechanics, biology, and physics to address various applied problems. One particular application involves describing moisture transfer dynamics in subsoil layers using pseudo-parabolic equations. This manuscript examines the inverse problem (IP) of identifying the moisture transfer function, along with the time-varying potential and source control terms, in a linear pseudo-parabolic equation from known moisture moments. We prove the existence of a unique solution to the inverse problem for sufficiently small times by employing the contraction principle. The inverse problem is reformulated as a nonlinear least-squares minimization problem, with the unknowns subjected to simple bounds. To guarantee stability, the Tikhonov regularization technique is utilized. For the numerical discretization, we develop the Crank-Nicolson finite-difference method to solve the direct problem. To solve the nonlinear least-squares minimization problem, we utilize the built-in subroutine lsqnonlin from the MATLAB optimization toolbox. We present and thoroughly discuss numerical outcomes for a benchmark test example, providing insights into the performance and effectiveness of the proposed methodology.
Açıklama
Anahtar Kelimeler
Fourier method, inverse problem, moisture moment, nonlinear optimization, pseudo-parabolic equation, Tikhonov regularization
Kaynak
Mathematical Methods in The Applied Sciences
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
47
Sayı
7
