Remark on a weakly coupled system of nonlinear damped wave equations

Nakao Hayashi, Pavel I. Naumkin, Masayo Tominaga

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study global existence of small solutions to the Cauchy problem for a weakly coupled nonlinear damped wave equation{(∂2t+∂t-δ)u=N1(v), (∂2t+∂t-δ)v=N2(u),x∈Rn, t>0 u(0,x)=εu0(x), ∂tu(0,x)=εu1(x), v(0,x)=εv0(x), ∂tv(0,x)=εv1(x), x∈Rn, with super-critical nonlinearities Nk(ϕ)=|ϕ|ρk, k= 1, 2, where ε>0, the space dimension n≥4. Our purpose is to remove the exponential decay condition on the data and the lower bound for ρ1 which was assumed in [4] when proving the global existence of solutions in the case of higher space dimensions.

Original languageEnglish
Pages (from-to)490-501
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume428
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • A weakly coupled system
  • Global existence
  • Super-critical case
  • System of damped wave equations
  • Time decay

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Remark on a weakly coupled system of nonlinear damped wave equations'. Together they form a unique fingerprint.

  • Cite this