Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects
In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations ü(t) + γ(t) + ∇ϕ(u(t)) + A(u(t)) = 0, where ∇ϕ is the gradient operator of a convex differentiable potential function ϕ: ,A: is a maximal monotone operator which is assumed to beλ-cocoercive, and γ > 0 is a damping parameter. Potential and non-potential effects are associated respectively to ∇ϕ and A. Under condition...