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Convergence and speed estimates for semilinear wave systems with nonautonomous damping
Author(s) -
Jiao Zhe,
Xiao TiJun
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3931
Subject(s) - dissipative system , mathematics , convergence (economics) , nonlinear system , infinity , mathematical analysis , exponent , control theory (sociology) , sine wave , physics , control (management) , computer science , linguistics , philosophy , quantum mechanics , artificial intelligence , economics , economic growth , voltage
We study the convergence to equilibria, as time tends to infinity, of trajectories of dissipative wave systems with time‐dependent velocity feedbacks and subject to nonlinear potential energies. Estimates for the speed of convergence are obtained in terms of the damping coefficient and the Łojasiewicz–Simon exponent. We allow for both restoring and amplifying effects of exterior forces, which makes our results possess wide applicability. As an example of application, we show that the trajectories of a sine‐Gordon system, with nonautonomous damping, approach equilibria at least polynomially. Copyright © 2016 John Wiley & Sons, Ltd.