## Differential and Integral Equations

### Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension

Kazunori Moriyama

#### Abstract

We prove that for small initial data there exist unique global solutions to a certain special class of nonlinear Klein-Gordon equations with cubic nonlinearity in one space dimension, which asymptotically approach the free solution of the linear Klein-Gordon equation as $t \to + \infty$.

#### Article information

Source
Differential Integral Equations, Volume 10, Number 3 (1997), 499-520.

Dates
First available in Project Euclid: 2 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367525665

Mathematical Reviews number (MathSciNet)
MR1744859

Zentralblatt MATH identifier
0892.35136

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35L10: Second-order hyperbolic equations

#### Citation

Moriyama, Kazunori. Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension. Differential Integral Equations 10 (1997), no. 3, 499--520. https://projecteuclid.org/euclid.die/1367525665