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(ohm). We obtain an approximated solution using the Fourier series truncation method and the terminal input data in Lq(ohm) 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(ohm); wherein an embedding between Lq(ohm) and Hilbert scale spaces H rho(ohm) is applied.