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Volume 53, Issue 3
Asymptotic Decomposition for Nonlinear Damped Klein-Gordon Equations

Ze Li & Lifeng Zhao

DOI: 10.4208/jms.v53n3.20.06

J. Math. Study, 53 (2020), pp. 329-352.

Published online: 2020-05

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  • Abstract

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 "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.

  • Keywords

Nonlinear Klein-Gordon equations, damping, soliton resolution, global attractor.

  • AMS Subject Headings

35Q60, 37N20, 35L10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rikudosennin@163.com (Ze Li)

zhaolf@ustc.edu.cn (Lifeng Zhao)

  • BibTex
  • RIS
  • TXT
@Article{JMS-53-329, author = {Li , Ze and Zhao , Lifeng}, title = {Asymptotic Decomposition for Nonlinear Damped Klein-Gordon Equations}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {3}, pages = {329--352}, abstract = {

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 "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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n3.20.06}, url = {http://global-sci.org/intro/article_detail/jms/16923.html} }
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 -

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 "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.

Li , Ze and Zhao , Lifeng. (2020). Asymptotic Decomposition for Nonlinear Damped Klein-Gordon Equations. Journal of Mathematical Study. 53 (3). 329-352. doi:10.4208/jms.v53n3.20.06
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