Optimal decay rates for nonlinear Moore–Gibson–Thompson equation with memory and Neumann boundary

We consider the initial value problem of Moore–Gibson–Thompson equation with memory effect, being subject to the Neumann boundary condition. Here, the nonlinearity f is conservative and satisfies some polynomial growth conditions. Under the condition that g(t) decays exponentially, we obtain the uniform polynomial decaying rate of energy and the solution. Moreover, we show this decay rate is optimal in the sense that there exists a class of solutions decaying exactly at this rate.