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

Let ΩΩ represent a two-dimensional isotropic elastic body. We consider the problem of determining the body force FF whose form φ(t)(f1(x),f2(x))φ(t)(f1(x),f2(x)) with φφ 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.