TY - JOUR
T1 - Asymptotic Decomposition for Nonlinear Damped Klein-Gordon Equations
AU - Li , Ze
AU - Zhao , Lifeng
JO - Journal of Mathematical Study
VL - 3
SP - 329
EP - 352
PY - 2020
DA - 2020/05
SN - 53
DO - http://doi.org/10.4208/jms.v53n3.20.06
UR - https://global-sci.org/intro/article_detail/jms/16923.html
KW - Nonlinear Klein-Gordon equations, damping, soliton resolution, global attractor.
AB - <p style="text-align: justify;">In this paper, we prove that if the solution to the damped focusing Klein-Gordon equations is global forward in time with bounded trajectory, then it will decouple into the superposition of divergent equilibriums. The core ingredient of our proof is
the existence of the &quot;concentration-compact attractor” introduced by Tao which yields
a finite number of asymptotic profiles. Using the damping effect, we can prove all the
profiles are equilibrium points.</p>