Hokkaido Mathematical Journal

Sunagawa Hideaki,

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

Hokkaido Mathematical Journal, 37 (2008) pp.825-838

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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.

MSC(Primary)35B30
MSC(Secondary)35B40, 35L67, 35L70, 35Q55
Uncontrolled Keywordslifespan, nonlinear Schrödinger equations, nonlinear Klein-Gordon equations.