On a Nonlocal Inverse Boundary Value Problem for the Sixth-Order Boussinesq Equation with Nonlocal Time Integral Conditions of the Second Kind

A classical solution of a nonlinear inverse boundary value problem for the sixth-order Boussinesq equation with double dispersive term under nonlocal time integral conditions of the second kind is studied. The problem essentially consists in determining not only the solution but also the unknown coefficients. It is considered in a rectangular area. The original inverse boundary value problem is solved by passing to an auxiliary inverse problem. The existence and uniqueness of a solution to this auxiliary problem are proved by using compression mappings. The transition back to the original inverse problem leads to the conclusion that the original inverse problem is solvable.