Long time existence for the quadratic wave equation associated to the harmonic oscillator. (January 2016)

• Record Type: Journal Article
• Authors: Zhang, Qidi
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 202
• Page End: 213
• Publication Date: 2016-01
• Subjects: 35L70 -- 35J15; Long time existence -- Harmonic oscillator -- Wave equations; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.10.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show the solution for the quadratic wave equation associated to the harmonic oscillator exists over a longer time interval than the one given by local existence theory. The key point is that the nonlinearity is quadratic so that we can estimate the small divisor and perform a normal form process.