Inverse problem for nonlinear partial differential equation with high order pseudoparabolic operator

We consider the questions of generalized solvability of inverse problem for nonlinear partial differential equations with high order pseudoparabolic operator by method of separation of variables. The mixed problem is reduced to the Volterra integral equation of the second kind, and the inverse problem — to the system of Volterra integral equations. The unique solvability of the inverse problem and the stability of its solution are proved.