Decay rates for the Moore-Gibson-Thompson equation with memory

The main goal of this paper is to investigate the existence and stability solutions for Moore–Gibson–Thompson equation (MGT) with a memory term in whole spaces \begin{document}$ \mathbb{R}^{N} $\end{document}. The MGT arises from modeling high-frequency ultrasound waves as an alternative model well-known Kuznetsov's equation. First, following [8] rid="b26">26], we show that problem well-posed under appropriate assumption on coefficients system. Then, built some Lyapunov functionals by using energy method Fourier space. These allows us get control estimates image solution. together integral inequalities lead decay rate id="M2">\begin{document}$ L^{2} $\end{document}-norm We use two types here: type ? ? term. Decay rates are obtained both types. More precisely, solution depending exponential or polynomial kernel. importantly, cases: subcritical range parameters critical range. However case has regularity-loss property.