On a non-local inverse boundary value problem for the sixth-order boussinesq equation with non-local time integral conditions of the second kind

In this paper, studies the classical solution of a nonlinear inverse boundary value problem for the Boussinesq equation of the sixth order with double variance with nonlocal time integral conditions of the second kind. The essence of the problem is that it is required to determine an unknown coefficients together with the solution. The problem is considered in a rectangular area. When solving the original inverse boundary value problem, a transition is made from the original inverse problem to some auxiliary inverse problem. With the help of compressed maps, the existence and uniqueness of the solution of the auxiliary problem are proved. Then the transition to the original inverse problem is made again, as a result, a conclusion is made about the solvability of the original inverse problem.