ASYMPTOTICS FOR A DISSIPATIVE DYNAMICAL SYSTEM WITH LINEAR AND GRADIENT-DRIVEN DAMPING
2013 ◽
Vol 18
(5)
◽
pp. 654-674
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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.
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2007 ◽
Vol 365
(1-2)
◽
pp. 17-27
◽
2002 ◽
Vol 81
(8)
◽
pp. 747-779
◽
2000 ◽
Vol 02
(01)
◽
pp. 1-34
◽
2007 ◽
Vol 5
◽
pp. 195-200
2021 ◽
Vol 1963
(1)
◽
pp. 012129
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