Volume 5 (2021) Issue 1

In this paper, we are concerned with the existence and uniqueness of global strong solution of non-planar oscillations for a nonlinear coupled Kirchhoff beam equations with moving boundary.

The double dispersive wave equation with memory and source terms $u_{tt}-\mathrm{\Delta }u-\mathrm{\Delta }{u}_{tt}+{\mathrm{\Delta }}^{2}u-{\int }_0^{t}g(t-\tau ){\mathrm{\Delta }}^{2}u(\tau )d\tau -\mathrm{\Delta }{u}_t=|u{|}^{p-2}u$ is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.