Asymptotic decomposition for nonlinear damped Klein-Gordon equations

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.

22pages, we correct some errors

Cited by in corpus (2)

• Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
• Long time behaviors for 3D cubic damped Klein-Gordon equations in inhomogeneous mediums