Polynomial Decay of Solutions to the Cauchy Problem for a Petrovsky–Petrovsky System in R n $\mathbb{R}^{n}$

Abstract

This paper describes a polynomial decay rate of solution for a coupled system of Petrovsky equations in Rn$\mathbb{R}^{n}$ with infinite memory acting in the first equation. The weighted spaces and results in Guesmia (Appl. Anal. 94(1):184---217, 2015) are also used. The main contributions here is to show that the infinite memory lets our problem still dissipative and that the system is not exponentially stable in spite of the kernel in the memory term is sub-exponential.