Regularization of a Nonstandard Cauchy Problem for a Dynamic Lame System

We consider the Cauchy problem for dynamic Lame systems in the cylinder G_T = D × (0,T) constructed over a domain D in a three-dimensional space, where the initial data are given in some strip in the lateral surface of the cylinder. The strip has the form S × (0,T), where S is an open subset of the boundary surface of the domain D. This problem is ill-posed. Under certain requirements to the configuration of S, we derive an explicit formula for solutions to this problem.

     

The Cauchy problem of the moment elasticity theory in R m

In this paper we consider the problem of analytical continuation of the solution to the system of equations of the moment theory of elasticity in spatial many-dimensional domain. We give an explicit formula of restoring of solution inside the domain by values of sought-for solution and values of strains on part of the boundary of this domain.