General energy decay and exponential instability to a nonlinear dissipative-dispersive viscoelastic Petrovsky equation

This work is concerned with the initial boundary value problem for a nonlinear viscoelastic Petrovsky wave equation Under suitable conditions on the relaxation function g, the global existence of solutions is obtained without any relation between m and p. The uniform decay of solutions is proved by adapting the perturbed energy method. For p > m and sufficient conditions on g, an unbound- edness result of solutions is also obtained.