Asymptotic behavior of a nonlinear Kirchhoff type equation with spring boundary conditions

In this paper, we consider the initial-boundary value problem for a nonlinear Kirchhoff type equation with the damping term and spring boundary conditions. We establish the global existence and uniqueness of solutions to this problem in time, and give an example and simulation to illustrate our results. For the proof, we use the Faedo–Galerkin approximate method. Finally, we study the asymptotic behavior of solutions and some of its simulation results. Results of this paper are able to apply industrial parts such as a typical model widely used to represent threads, wires, magnetic tapes, belts, band saws, and so on.