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VOL. 85 | 2020 Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping
Ning-An Lai, Nico Michele Schiavone, Hiroyuki Takamura

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

Abstract

In this paper we study blow-up and lifespan estimate for solutions to the Cauchy problem with small data for semilinear wave equations with scattering damping and negative mass term. We show that the negative mass term will play a dominant role when the decay of its coefficients is not so fast, thus the solutions will blow up in a finite time. What is more, we establish a lifespan estimate from above which is much shorter than the usual one.

Information

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

Digital Object Identifier: 10.2969/aspm/08510391

Subjects:
Primary: 35L71
Secondary: 35B44

Rights: Copyright © 2020 Mathematical Society of Japan

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