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

Let Ω represent a two-dimensional isotropic elastic body. We consider the problem of determining the body force F whose form φ ( t ) ( f 1 ( x ) , f 2 ( x ) ) with φ 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 explicitly derive the error estimate.