Well-posedness for a class of wave equation with past history and a delay (Q286423)

The study refers to a wave equation with past history, inhomogeneous, with a source term and a linear dumping and delay. Attached to the model are some initial and boundary conditions. The energy functional is defined. Under some special assumptions for the memory kernel, the nonlinear source term and the initial data, the existence of a unique weak solution, continuously depending on the initial data, is proved. Further, an exponential stability result for the energy to the problem is shown.