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September/October 2018 A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity
Yuji Sagawa, Hideaki Sunagawa, Shunsuke Yasuda
Differential Integral Equations 31(9/10): 685-700 (September/October 2018).

Abstract

Let $T_{\varepsilon}$ be the lifespan for the solution to the Schrödinger equation on $\mathbb R^d$ with a power nonlinearity $\lambda |u|^{2\theta/d}u$ ($\lambda \in \mathbb C$, $0< \theta < 1$) and the initial data in the form $\varepsilon \varphi(x)$. We provide a sharp lower bound estimate for $T_{\varepsilon}$ as $\varepsilon \to +0$ which can be written explicitly by $\lambda$, $d$, $\theta$, $\varphi$ and $\varepsilon$. This is an improvement of the previous result by H. Sasaki [Adv. Diff. Eq., 14 (2009), 1021-1039].

Citation

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Yuji Sagawa. Hideaki Sunagawa. Shunsuke Yasuda. "A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity." Differential Integral Equations 31 (9/10) 685 - 700, September/October 2018.

Information

Published: September/October 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06945777
MathSciNet: MR3814562

Subjects:
Primary: 35B40, 35Q55

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 9/10 • September/October 2018
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