On a coupled system of viscoelastic wave equation of infinite memory with acoustic boundary conditions

Abstract

This work deals with a coupled system of viscoelastic wave equation of infinite memory with mixed Dirichlet-Neumann boundary conditions. The coupling is via the acoustic boundary conditions on a portion of the boundary. The semigroup theory is used to show the well-posedness and regularity of the initial and boundary value problem. Moreover, we investigate exponential stability of the system taking into account Gearhart-Prüss’s theorem. Mathematics Subject Classification (2010): 35A01, 74B05, 93D15. Received 11 June 2021; Accepted 13 October 2021