Abstract
In this paper, we prove the long time behavior of bounded solutions to a first order gradient-like system with low damping and perturbation terms. Our convergence results are obtained under some hypotheses of KurdykaLojasiewicz inequality and the angle and comparability condition.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.
Highlights
Our convergence results are obtained under some hypotheses of KurdykaLojasiewicz inequality and the angle and comparability condition
The main goal of this paper is to obtain the asymptotic behavior of bounded solutions to the gradient-like system as follows u0 (t)+γ(t)u(t)+G(u(t)) = f (t), t ∈ [0, ∞), (1)on the long time behavior of the trajectories u.This type of problem have been studied in many recent papers with dierent assumptions of G
We prove the long time behavior of bounded solutions to a rst order gradient-like system with low damping and perturbation terms
Summary
Our convergence results are obtained under some hypotheses of KurdykaLojasiewicz inequality and the angle and comparability condition. The main goal of this paper is to obtain the asymptotic behavior of bounded solutions to the gradient-like system as follows u0 (t)+γ(t)u(t)+G(u(t)) = f (t), t ∈ [0, ∞), (1) They proved that the bounded solution converges to an equilibrium as t goes to innity if the function F is real analytic in [18].
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