Regularization of a nonstandard Cauchy problem for a dynamic Lame system

We consider a Cauchy problem for the dynamic systems Lame in a cylinder $G_T=D\times(0,T)$ over a domain $D$ in $R^3$ with data on a strip lying on the lateral surface. The strip is of the form $S\times(0,T)$, where $S-$ is an open subset of the boundary of $D$. The problem is ill-posed. Under natural restrictions on the configuration of $S$ we derive an explicit formula for solutions of this problem.