Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey’s conjecture

Ning An Lai, Hiroyuki Takamura

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalDifferential and Integral Equations
Volume32
Issue number1-2
Publication statusPublished - 2019 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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