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