Cauchy Problem for Dynamic ElasticityEquations

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.

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