Abstract
We study the global existence and time decay of solutions to nonlinear dispersive wave equations ∂2 t u + 1/ρ2(-Δ)ρ u = F (∂tu) in two space dimensions, where F (∂tu) = λ∂tup-1∂tu or λ∂tup-, λ∈ C; with p > 2 for 0 < ρ < 1; p > 3 for ρ = 1; and p > 1 + ρ for 1 < ρ < 2: If ρ = 1; then the equation converts into the well-known nonlinear wave equation.
Original language | English |
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Pages (from-to) | 1377-1393 |
Number of pages | 17 |
Journal | Communications on Pure and Applied Analysis |
Volume | 14 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2015 Jul 1 |
Externally published | Yes |
Keywords
- Asymptotic behavior
- Dispersive nonlinear wave
- Global in time of solutions
- System of equations
- Vector field method
ASJC Scopus subject areas
- Analysis
- Applied Mathematics