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Asymptotic decomposition for nonlinear damped Klein-Gordon equations (1511.00437v3)
Published 2 Nov 2015 in math.AP
Abstract: 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.
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