Existence and decay rates for a coupled Balakrishnan‐Taylor viscoelastic system with dynamic boundary conditions

Abstract

In this paper, we are concerned with a coupled viscoelastic wave system with Balakrishnan‐Taylor dampings, dynamic boundary conditions, source terms, and past histories. Under suitable assumptions on relaxation functions and source terms, we prove the global existence of solutions by potential well theory and we establish a more general decay result of energy, in which the exponential decay and polynomial decay are only special cases, by introducing suitable energy and perturbed Lyapunov functionals.