Well‐posedness and exponential decay for the Moore–Gibson–Thompson equation with time‐dependent memory kernel

We are interested in the well‐posedness and exponential decay of Moore–Gibson–Thompson equation with memory Here, the main feature is that the memory kernel depends on time. By using the linear semigroup theory, we prove that the above system is global well‐posedness. In addition, the exponential decay of the related energy is shown to occur, provided that the memory kernel is controlled by a negative exponential.