Qualitative properties of solution to a viscoelastic Kirchhoff-like plate equation

Abstract

This paper is concerned with the initial boundary value problem for viscoelastic Kirchhoff-like plate equations with rotational inertia, memory, p-Laplacian restoring force, weak damping, strong damping, and nonlinear source terms. We establish the local existence and uniqueness of the solution by linearization and the contraction mapping principle. Then, we obtain the global existence of solutions with subcritical and critical initial energy by applying potential well theory. Then, we prove the asymptotic behavior of the global solution with positive initial energy strictly below the depth of the potential well. Finally, we conduct a comprehensive study on the finite time blow-up of solutions with negative initial energy, null initial energy, and positive initial energy strictly below the depth of the potential well and arbitrary positive initial energy, respectively.