On an inverse boundary value problem for the sixth-order Boussinesq equation with integral conditions

This work investigates the inverse boundary value problem for a sixth-order Boussinesq equa-tion, where the time-dependent coefficients are unknown. The primary objective is to determine these unknown coefficients and solve the corresponding problem. The original problem is transformed into an equivalent auxiliary problem. By utilizing the contraction mapping method, we prove the existence and uniqueness of the solution for the auxiliary problem. Consequently, we establish the existence and uniqueness of a classical solution to the initial problem.