An extensible beam equation of Kirchhoff type with internal damping and source term is investigated. We apply the potential well and establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations, taking into account that the initial data is located in a suitable set of stability created from the Nehari manifold. Moreover, by using Nakao’s method, we prove the exponential stability of the solution for \(p=1\) and the polynomial stability for \(p>1\).
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Pereira, D.C., Raposo, C.A., Maranhão, C.H.M. et al. Global Existence and Uniform Decay of Solutions for a Kirchhoff Beam Equation with Nonlinear Damping and Source Term. Differ Equ Dyn Syst (2021). https://doi.org/10.1007/s12591-021-00563-x
- Extensible beam
- Potential well
Mathematics Subject Classification