On an inverse problem for a nonlinear third order in time partial differential equation
[ X ]
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier B.V.
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this article, first we convert an inverse problem of determining the unknown timewise terms of nonlinear third order in time partial differential equation (PDE) from knowledge of two boundary measurements to the auxiliary system of integral equations. Then, existence and uniqueness of the solution of this system is proved by means of the contraction principle on a small time interval. Also uniqueness of the solution of the inverse problem is given. However, since the governing equation is yet ill-posed (very slight errors in the temperature input may cause relatively significant errors in the output potential and source terms), we need to regularize the solution. Therefore, to get a stable solution, a regularized cost function is to be minimized for retrieval of the unknown terms. The third order in time PDE problem is discretized using the FDM and reshaped as non-linear least-squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Both analytical and perturbed data are inverted. Numerical outcomes for two benchmark test examples are reported and discussed. The proposed numerical approach has also been discussed. © 2022 The Author(s)
Açıklama
Anahtar Kelimeler
Existence and uniqueness, Inverse problems for PDEs, Nonlinear optimization, Third order in time PDE, Tikhonov regularization
Kaynak
Results in Applied Mathematics
WoS Q Değeri
Scopus Q Değeri
Q2
Cilt
15
