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January/February 2019 Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture
Ning-An Lai, Hiroyuki Takamura
Differential Integral Equations 32(1/2): 37-48 (January/February 2019).

Abstract

This work is devoted to the nonexistence of global-in-time energy solutions of nonlinear wave equation of derivative type with weak time-dependent damping in the scattering and scale invariant range. By introducing some multipliers to absorb the damping term, we succeed in establishing the same upper bound of the lifespan for the scattering damping as the non-damped case, which is a part of so-called Glassey's conjecture on nonlinear wave equations. We also study an upper bound of the lifespan for the scale invariant damping with the same method.

Citation

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Ning-An Lai. Hiroyuki Takamura. "Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture." Differential Integral Equations 32 (1/2) 37 - 48, January/February 2019.

Information

Published: January/February 2019
First available in Project Euclid: 11 December 2018

zbMATH: 07031708
MathSciNet: MR3909978

Subjects:
Primary: 35B44, 35L71

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 1/2 • January/February 2019
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