Regularization of a Nonstandard Cauchy Problem for a Dynamic Lame System

We consider the Cauchy problem for dynamic Lame systems in the cylinder GT = 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.

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