Convergence of Solutions to the Equation of Quasi-Static Approximation of Viscoelasticity with Capillarity

The long time behavior of solutions to the quasi-steady approximation of the equation of viscoelasticity with capillarity is investigated. We consider the equation with a number of boundary conditions including such that the set of equilibria is necessarily at least one dimensional. We prove that any solution converges to an equilibrium point. We admit some kind of initial data with infinite energy. We use tools based on the assumption that the nonlinear term is real analytic.