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 language | English |
|---|---|
| Pages (from-to) | 490-501 |
| Number of pages | 12 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 428 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 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
Hayashi, N., Naumkin, P. I., & Tominaga, M. (2015). Remark on a weakly coupled system of nonlinear damped wave equations. Journal of Mathematical Analysis and Applications, 428(1), 490-501. https://doi.org/10.1016/j.jmaa.2015.03.008