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.

中文翻译：

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动态La腿系统非标准柯西问题的正则化

我们考虑了在三维空间中的域D上构造的圆柱体G _T = D ×（0，T）中的动态Lame系统的柯西问题，其中初始数据在圆柱体侧面的某些条带中给出。条带的形式为S ×（0，T），其中S是域D的边界表面的开放子集。这个问题是不恰当的。在对S的配置有一定要求的情况下，我们导出了用于解决此问题的明确公式。