Destruction of solutions of wave equations in systems with distributed parameters

摘要

We consider two initial boundary value problems on an interval with homogeneous Dirichlet conditions. These problems were proposed by M. I. Rabinovich and D. I. Trubetskov and are given by nonlinear fourth-order Sobolev-type equations. We prove the local-in-time existence of a strong generalized solution of one problem, and for both problems, we obtain sufficient conditions for the destruction of their strong generalized solutions in a finite time.