Asymptotic behavior for second order stochastic evolution equations with memory

Asymptotic behavior of second-order dynamic equations

We prove several growth theorems for second-order dynamic equations on time scales. These theorems contain as special cases results for second-order differential equations, difference equations, and q-difference equations. 2006 Elsevier Inc. All rights reserved.

The Asymptotic Behavior for Second-Order Neutral Stochastic Partial Differential Equations with Infinite Delay

Asymptotic Stability of Second-order Evolution Equations with Intermittent Delay

We consider second-order evolution equations in an abstract setting with intermittently delayed/not-delayed damping and give sufficient conditions ensuring asymptotic and exponential stability results. Our abstract framework is then applied to the wave equation, the elasticity system, and the Petrovsky system. For the Petrovsky system with clamped boundary conditions, we further prove an intern...

Asymptotic Stability for Intermittently Controlled Second-Order Evolution Equations

Motivated by several works on ordinary differential equations, we are interested in the asymptotic stability of intermittently controlled partial differential equations. We give a condition of asymptotic stability for second-order evolution equations uniformly damped by an on/off feedback. This result extends to the case of partial differential equations a previous result of R. A. Smith concern...

Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects

In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations ü(t) + γu̇(t) +∇φ(u(t)) +A(u(t)) = 0, where ∇φ is the gradient operator of a convex differentiable potential function φ : H → IR, A : H → H is a maximal monotone operator which is assumed to be λ-cocoercive, and γ > 0 is a damping param...