Study of a model for the equations of inserted elastic string in a thermal environment (Q1887990)

The authors consider the existence of a global solution and the asymptotic behavior of the corresponding energy associated with nonlinear coupled system. They consider the Kirchhoff equation with strong damping of the type \((-\Delta)^\alpha u'\) and Neumann boundary conditions coupled with the heat equation. The coupling of the heat equation in the model of vibrations presents important aspects because it represents better the reality beyond, allowing to control the vibrations in a more adequate way, since removing the strong damping \((-\Delta)^\alpha u'\), in the system, they still get the exponential decay of their problem due to the contribution of the heat.