On the Moore-Gibson-Thompson Equation with Memory with Nonconvex Kernels

We consider the MGT equation with memory ∂tttu + α ∂ttu - β∆ ∂tu - γ∆u +Z0t g(s)∆u(t - s)ds = 0. We prove an existence and uniqueness result removing the convexity assumption on the convolution kernel g, usually adopted in the literature. In the subcritical case αβ > γ, we establish the exponential decay of the energy, without leaning on the classical differential inequality involving g and its derivative g′, namely, g′ + δg ≤ 0, δ > 0, but we ask only that g vanish exponentially fast.