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June 2021 Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension
Jun-ichi SEGATA
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Hokkaido Math. J. 50(2): 187-205 (June 2021). DOI: 10.14492/hokmj/2018-938

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 $L^{\infty}$ decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).

Acknowledgment

We thank the referee for careful reading of the manuscript and for fruitful suggestions. J.S was supported by JSPS KAKENHI Grant Number JP17H02851.

Citation

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Jun-ichi SEGATA. "Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension." Hokkaido Math. J. 50 (2) 187 - 205, June 2021. https://doi.org/10.14492/hokmj/2018-938

Information

Received: 29 November 2018; Revised: 25 February 2020; Published: June 2021
First available in Project Euclid: 27 August 2021

Digital Object Identifier: 10.14492/hokmj/2018-938

Subjects:
Primary: 35L71
Secondary: 35B40, 81Q05

Rights: Copyright c 2021 Hokkaido University, Department of Mathematics

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Vol.50 • No. 2 • June 2021
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