Long-time behavior of a semilinear wave equation with memory

Baowei Feng, Maurício L Pelicer, Doherty Andrade
2016 Boundary Value Problems  
In this paper we study the long-time dynamics of the semilinear viscoelastic equation defined in a bounded domain of R 3 with Dirichlet boundary condition. The functions f = f (u) and h = h(x) represent forcing terms and the kernel function μ ≥ 0 is assumed to decay exponentially. Then, by exploring only the dissipation given by the memory term, we establish the existence of a global attractor to the corresponding dynamical system. MSC: 35L71; 35B41; 74D99
doi:10.1186/s13661-016-0551-5 fatcat:moc53ca4ljholl2mkv4h7abydi