Hokkaido Mathematical Journal

The lifespan of solutions to nonlinear Schrödinger and Klein-Gordon equations

Hideaki SUNAGAWA

Full-text: Open access

Abstract

Precise information on the lifespan sometimes tells us how the nonlinearity affects large time behavior of solutions to nonlinear evolution equations. As pointed out by John and Hörmander in 1987, there are surprising connections between the lifespan and the null condition in the wave equation case. In this paper we give a review of analogous lifespan estimates for nonlinear Schrödinger and Klein-Gordon equations. We also discuss how this viewpoint could give a unified understanding of many previous results.

Article information

Source
Hokkaido Math. J., Volume 37, Number 4 (2008), 825-838.

Dates
First available in Project Euclid: 31 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1249046371

Digital Object Identifier
doi:10.14492/hokmj/1249046371

Mathematical Reviews number (MathSciNet)
MR2474178

Zentralblatt MATH identifier
1178.35087

Subjects
Primary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]
Secondary: 35B40: Asymptotic behavior of solutions 35L67: Shocks and singularities [See also 58Kxx, 76L05] 35L70: Nonlinear second-order hyperbolic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
lifespan nonlinear Schrödinger equations nonlinear Klein-Gordon equations

Citation

SUNAGAWA, Hideaki. The lifespan of solutions to nonlinear Schrödinger and Klein-Gordon equations. Hokkaido Math. J. 37 (2008), no. 4, 825--838. doi:10.14492/hokmj/1249046371. https://projecteuclid.org/euclid.hokmj/1249046371


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