Abstract
We consider the following abstract version of the Moore-Gibson-Thompson (MGT) equation:
au(ttt) + beta u(tt) + c(2)Delta u + b Delta u(t) +integral(t)(0)h(t - s)Delta u(s)ds = 0,
depending on the parameters a, beta, b > 0, and h is a convex and nonnegative memory kernel. The related energy has been shown to decay exponentially by Boulaaras et al., Math. Meth. Appl. Sci. 42 (2019) 2664-2679; Lasiecka et al., Z. Angew. Math. Phys. 67 (2016) 17. Here, in this original work, the solvability of the abstract version of nonlocal mixed boundary value problem for the MGT equation via Galerkin's method is discussed.