Differential and Integral Equations

Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension

Hideaki Sunagawa

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Abstract

We study the large time behavior of the solution to the Cauchy problem for the one-dimensional, cubic nonlinear Klein-Grodon equation with complex-valued initial data. We show that the small amplitude solution decays like $t^{-1/2}$ as $t$ tends to infinity. Several remarks are also given on the large time asymptotics.

Article information

Source
Differential Integral Equations, Volume 18, Number 5 (2005), 481-494.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060181

Mathematical Reviews number (MathSciNet)
MR2136975

Zentralblatt MATH identifier
1212.35318

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35L15: Initial value problems for second-order hyperbolic equations

Citation

Sunagawa, Hideaki. Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension. Differential Integral Equations 18 (2005), no. 5, 481--494. https://projecteuclid.org/euclid.die/1356060181


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