Damped wave equation with a critical nonlinearity in higher space dimensions

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity |u|u, where n denotes the space dimension. For n=1,2,3, global in time existence of small solutions was shown in [4]. In this paper, we generalize the results to any spatial dimension via the method of decomposition of the equation into the high and low frequency components under the assumption that the initial data are small and decay rapidly at infinity. Furthermore we present a sharp time decay estimate of solutions with a logarithmic correction.

Original languageEnglish
Pages (from-to)801-822
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume446
Issue number1
DOIs
Publication statusPublished - 2017 Feb 1
Externally publishedYes

Keywords

  • Critical nonlinearity
  • Damped wave equation
  • Higher space dimension
  • Large time asymptotics

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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