Asymptotic Behavior In Time Of Solutions To Complex-Valued Nonlinear Klein-Gordon Equation In One Space Dimension

Jun Ichi Segata

doi:10.14492/HOKMJ/2018-938

Asymptotic Behavior In Time Of Solutions To Complex-Valued Nonlinear Klein-Gordon Equation In One Space Dimension

Jun Ichi Segata

Research output: Contribution to journal › Article › peer-review

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Abstract

We consider the long time behavior of solutions to the initial value problem for the \complex-valued" cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the L 1 decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).

Original language	English
Pages (from-to)	187-205
Number of pages	19
Journal	Hokkaido Mathematical Journal
Volume	50
Issue number	2
DOIs	https://doi.org/10.14492/HOKMJ/2018-938
Publication status	Published - 2021

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.14492/HOKMJ/2018-938

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title = "Asymptotic Behavior In Time Of Solutions To Complex-Valued Nonlinear Klein-Gordon Equation In One Space Dimension",

abstract = "We consider the long time behavior of solutions to the initial value problem for the \complex-valued{"} cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the L 1 decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).",

author = "Segata, {Jun Ichi}",

note = "Funding Information: uscript and for fruitful suggestions. J.S was supported by JSPS KAKENHI GrantNumberJP17H02851. Publisher Copyright: {\textcopyright} 2021,Hokkaido Mathematical Journal.All Rights Reserved",

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AB - We consider the long time behavior of solutions to the initial value problem for the \complex-valued" cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the L 1 decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).

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Asymptotic Behavior In Time Of Solutions To Complex-Valued Nonlinear Klein-Gordon Equation In One Space Dimension

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