The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative-Reference-Cited by-同舟云学术

The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative

Published:2023 Issue:11 Volume:8 Page:25477-25486
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Sasaki Takiko¹²,Takamatsu Shu³,Takamura Hiroyuki²

Affiliation:

1. Department of Mathematical Engineering, Faculty of Engineering, Musashino University, 3-3-3 Ariake, Koto-ku, Tokyo 135-8181, Japan

2. Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

3. Master course, Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Abstract

<abstract><p>This paper is devoted to the lifespan estimates of small classical solutions of the initial value problems for one dimensional wave equations with semilinear terms of the spatial derivative of the unknown function. It is natural that the result is same as the one for semilinear terms of the time-derivative. But there are so many differences among their proofs. Moreover, it is meaningful to study this problem in the sense that it may help us to investigate its blow-up boundary in the near future.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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