Determination of the body force of a two-dimensional isotropic elastic body

Let $\mathrm{\Omega }$ represent a two$-$dimensional isotropic elastic body. We consider the problem of determining the body force $F$ whose form $\varphi (t)(f_1(x),f_2(x))$ with $\varphi$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov’s regularization and truncated integration, we construct a regularized solution from the data given inexactly and derive the explicitly error estimate. Numerical part is given