Advanced Mathematical Models & Applications

The paper investigates the existence and uniqueness of the solution to a third-order hyperbolic equation describing the propagation of longitudinal waves in a dispersive medium with nonclassical boundary conditions. First some necessary auxiliary facts are presented. Then the original problem is transformed into an equivalent formulation with trivial boundary conditions. Using the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to this system are established using the contraction mapping principle. Finally, based on the equivalence of these problems, the existence and uniqueness of the classical solution to the original problem are demonstrated.