General Decay Rate for a Moore–Gibson–Thompson Equation with Infinite History

In previous work (Alves et al. in Z Angew Math Phys 69:106, 2018), by using the linear semigroup theory, Alves et al. investigated the existence and exponential stability results for a Moore–Gibson–Thompson model encompassing memory of type 1, 2 or 3 in a history space framework. In this paper, we continue to consider the similar problem with type 1 and establish explicit and general decay results of energy for system in both the subcritical and critical cases, by introducing suitable energy and perturbed Lyapunov functionals and following convex functions ideas presented in Guesmia (J Math Anal Appl 382:748–760, 2011). Our results allow a much larger class of the convolution kernels which improves the earlier related results.