General decay of the double dispersive wave equation with memory and source terms

The double dispersive wave equation with memory and source terms \(u_{tt}-\Delta u-\Delta u_{tt}+\Delta^{2}u-\int_{0}^{t}g(t-\tau)\Delta^{2}u(\tau)d\tau-\Delta u_{t}=|u|^{p-2}u \) is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.

Global solutions and general decay for the dispersive wave equation with memory and source terms

This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms

On Blow-Up Structures for a Generalized Periodic Nonlinearly Dispersive Wave Equation

The local well-posedness for a generalized periodic nonlinearly dispersive wave equation is established. Under suitable assumptions on initial valueu0, a precise blow-up scenario and several sufficient conditions about blow-up results to the equation are presented.