New general decay results for a Moore–Gibson–Thompson equation with memory

In this paper, we consider the Moore–Gibson–Thompson equation with a memory term in the subcritical case, which arises in high-frequency ultrasound applications accounting for thermal flux and molecular relaxation times. For a class of relaxation functions satisfying g′(t)≤−ξ(t)H(g(t)) for H to be increasing and convex function near the origin and ξ(t) to be a nonincreasing function, we establish the optimal explicit and general energy decay result, from which we can recover the earlier exponential rate in the special case.