Abstract:
We consider the Cauchy problem for one system unsolvable with respect to the highest time derivative. The system under study belongs to the class of pseudohyperbolic systems and describes transverse flexural-torsional vibrations of an elastic rod. We prove the unique solvability of the Cauchy problem in Sobolev spaces and obtain estimates for the solution.
Keywords:system unsolvable with respect to the highest time derivative, pseudohyperbolic system, transverse flexural-torsional vibrations.