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Original Articles

Asymptotics for a Dissipative Dynamical System with Linear and Gradient-Driven Damping

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Pages 654-674 | Received 22 Oct 2012, Accepted 12 Nov 2013, Published online: 24 Dec 2013
 

Abstract

We study, in the setting of a real Hilbert space H, the asymptotic behavior of trajectories of the second-order dissipative dynamical system with linear and gradient-driven nonlinear damping

where λ > 0 and f, Φ: H → R are two convex differentiable functions. It is proved that if Φ is coercive and bounded from below, then the trajectory converges weakly towards a minimizer of Φ. In particular, we state that under suitable conditions, the trajectory strongly converges to the minimizer of Φ exponentially or polynomially.

AMS Subject Classification:

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