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Asymptotic decomposition for nonlinear damped Klein-Gordon equations

In this paper, we proved that if the solution to damped focusing Klein-Gordon equations is global forward in time, then it will decouple into a finite number of equilibrium points with different shifts from the origin. The core ingredient of our proof is the existence of the "concentration-compact attractor" which yields a finite number of profiles. Using damping effect, we can prove all the profiles are equilibrium points.

preprint2015arXivOpen access
Ze LiLifeng Zhao
math.AP
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Ze LiLifeng Zhao

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