Asymptotic smoothness effects and global attractor for a peridynamic model with energy damping

Abstract

In this paper, we consider a peridynamic model with energy damping inspired by the works of Balakrishnan and Taylor on “damping models” based on the instantaneous total energy of the system. We study the asymptotic behavior of solutions, in the sense of attractors, of these peridynamic models in suitable phase space; more precisely, we prove a result of existence and characterization of compact global attractors with a nonlinear strongly continuous semigroup approach based in the asymptotic smoothness property thanks to Chueshov and Lasiecka and Nakao's lemma.