The body force in a three-dimensional Lame system: identification and regularization

Let a three-dimensional isotropic elastic body be described by the Lame system with the body force of the form F(x, t)=phi(t)f(x), where phi is known. We consider the problem of determining the unknown spatial term f (x) of the body force when the surface stress history is given as the overdetermination. This inverse problem is ill-posed. Using the interpolation method and truncated Fourier series, we construct a regularized solution from approximate data and provide explicit error estimates.