On a nonlinear inverse boundary value problem for linearized sixth-order boussinesq equation with an additional integral condition

Background. A huge number of mathematical models are called Boussinesq equations; therefore, a wide range of sixth-order Boussinesq equations attracts a lot of attention from outside researchers around the world. Materials and methods. The research studies the classical solution of one nonlinear inverse boundary value problem for linearized sixth-order Boussinesq equation with an additional integral condition. One method is based on the application of the Fourier method. The second method is to apply the method of compressed mappings. Results. The essence of the problem is that together with the solution it is required to determine an unknown coefficient depending on the variable t with an unknown function. The problem is considered in a rectangular area. When solving the original inverse boundary value problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out. The existence and uniqueness of a solution to an auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is again made, as a result, a conclusion is made about the solvability of the original inverse problem. Conclusions. The proposed methods for finding solutions to the inverse problem can be used in the study of solvability for various problems of mathematical physics.