TY - JOUR
T1 - Remark on a weakly coupled system of nonlinear damped wave equations
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
AU - Tominaga, Masayo
N1 - Funding Information:
We would like to thank the unknown referee for useful comments on the first draft. The work of N.H. is partially supported by JSPS KAKENHI Grant Number 25220702 . The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100113 .
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - A weakly coupled system
KW - Global existence
KW - Super-critical case
KW - System of damped wave equations
KW - Time decay
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U2 - 10.1016/j.jmaa.2015.03.008
DO - 10.1016/j.jmaa.2015.03.008
M3 - Article
AN - SCOPUS:84934435909
VL - 428
SP - 490
EP - 501
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -