Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions

Satoshi Masaki, Jun Ichi Segata

研究成果: Article査読

3 被引用数 (Scopus)

抄録

In this paper, we consider the long time behavior of the solution to the quadratic nonlinear Klein–Gordon equation (NLKG) in two space dimensions: (Formula Presented), where □ = ∂t 2 − Δ is d’Alembertian. For a given asymptotic profile uap, we construct a solution u to (NLKG) which converges to uap as t → ∞. Here the asymptotic profile uap is given by the leading term of the solution to the linear Klein–Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on Fourier series expansion of the nonlinearity.

本文言語English
ページ(範囲)8155-8170
ページ数16
ジャーナルTransactions of the American Mathematical Society
370
11
DOI
出版ステータスPublished - 2018

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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