The dynamic problem for reissner's one-dimensional system

The boundary-value problem is considered on the time interval [0T] for some system of nonlinear differential equations of the shell theory. An integro-differential equation is obtained with respect to one of the unknown functions w. Other unknown functions are expressed explicitly through w. It is shown that on a time interval [0T 0 ]T 0 ≤T, there exists a solution of the problem with respect to w. The problem of finding of T 0 is discussed.