@article{Nguyen2022, 
author = {Anh Tuan Nguyen and Le Dinh Long and Devendra Kumar and Van Thinh Nguyen},
title = {Regularization of a final value problem for a linear and nonlinear biharmonic equation with observed data in  Lq space},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {12},
pages = {20660-20683},
keywords = {biharmonic equations, Fourier truncation method, inverse problem, regularization, Sobolev embedding},
url = {https://www.sciopen.com/article/10.3934/math.20221133},
doi = {10.3934/math.20221133},
abstract = {In this work, we focus on the final value problem of an inverse problem for both linear and nonlinear biharmonic equations. The aim of this study is to provide a regularized method for the bi-harmonic equation, once the observed data are obtained at a terminal time in  Lq(Ω). We obtain an approximated solution using the Fourier series truncation method and the terminal input data in  Lq(Ω) for  q≠2. In comparision with previous studies, the most highlight of this study is the error between the exact and regularized solutions to be estimated in  Lq(Ω); wherein an embedding between  Lq(Ω) and Hilbert scale spaces  Hρ(Ω) is applied.}
}