Remark on a weakly coupled system of nonlinear damped wave equations

Nakao Hayashi, Pavel I. Naumkin, Masayo Tominaga

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2015


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


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