Decay and asymptotics for the one-dimensional klein-gordon equation with variable coefficient cubic nonlinearities

Hans Lindblad, Jonas Lührmann, Avy Soffer

Research output: Contribution to journalArticlepeer-review

Abstract

We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein-Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to deal with the long-range nature of the cubic nonlinearity become problematic in the presence of variable coefficients. We introduce a novel approach based on pointwise-in-time local decay estimates for the Klein-Gordon propagator to overcome this impasse.

Original languageEnglish (US)
Pages (from-to)6379-6411
Number of pages33
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number6
DOIs
StatePublished - Dec 18 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Asymptotic stability of kink solutions
  • Klein-Gordon equation
  • Long-range scattering
  • Variable coefficient nonlinearity

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