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) $ 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.