We consider the problem on the analytic continuation of the solution of the system of vibration equations in elasticity theory in a spatial domain based on the values of the solution and the stresses on part of the boundary of this domain, i.e., a Cauchy problem. The problem is ill posed. If the part of the domain on which the Cauchy data are given is real analytic, then the problem has a local solution by the Cauchy–Kovalevskaya theorem. The special structure of the vibration equation is used to obtain explicit global solvability conditions and construct approximate solutions.

中文翻译：

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动态弹性方程的柯西问题

我们考虑基于解的值和该域的部分边界上的应力，弹性理论中振动方程组的解在空间域中的解析延拓问题，即柯西问题。问题不妙。如果给出柯西数据的域的部分是实解析的，那么根据柯西-科瓦列夫斯卡亚定理，该问题具有局部解。振动方程的特殊结构用于获得明确的全局可解性条件并构造近似解。