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VOL. 85 | 2020 Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity
Hayato Miyazaki

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

This paper is a survey article to review the Cauchy problem for the generalized KdV equation with low-degree of nonlinearity. In [5], the local well-posedness for the equation is established in an appropriate class under a non-degenerate condition for the initial data. In this paper, we give a lower bound estimate for the lifespan of the solution under the condition as a consequence of the contraction principle. The lifespan depends on the size and a quantity corresponding to the distance from zero of the initial data.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510303

Subjects:
Primary: 35Q53
Secondary: 35A01

Rights: Copyright © 2020 Mathematical Society of Japan

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