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

Abstract

Let a three-dimensional isotropic elastic body be described by the Lamé system with the body force of the form $F(x,t)=ϕ(t)f(x)$, where $ϕ$ is known. We consider the problem of determining the unknown spatial term $f(x)$ of the body force where 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. AMS 2010 Subject Classification: 35L20, 35R30. Keywords: Body force, elastic, ill$-$posed problem, interpolation, Fourier series.