An inverse problem for a fourth-order Boussinesq equation with non-conjugate boundary and integral overdetermination conditions

The work is devoted to the study of the solvability of the inverse boundary value problem with an unknown time depended coefficient for a fourth-order Boussinesq equation with non-conjugate boundary conditions and integral overdetermination conditions. The goal of paper consists of determination of the unknown coefficient and the solution of the considered problem. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, we perform a conversion from the original problem to some direct auxiliary problem with trivial boundary conditions. Further, we prove the solvability of the supplementary inverse problem. Then we make a conversion to the stated problem again and as a result we receive the solvability of the inverse problem.