TY - JOUR
T1 - Nonlinear dispersive wave equations in two space dimensions
AU - Hayashi, Nakao
AU - Kobayashi, Seishirou
AU - Naumkin, Pavel I.
PY - 2015/7/1
Y1 - 2015/7/1
N2 - 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.
AB - 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.
KW - Asymptotic behavior
KW - Dispersive nonlinear wave
KW - Global in time of solutions
KW - System of equations
KW - Vector field method
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U2 - 10.3934/cpaa.2015.14.1377
DO - 10.3934/cpaa.2015.14.1377
M3 - Article
AN - SCOPUS:84969835778
SN - 1534-0392
VL - 14
SP - 1377
EP - 1393
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 4
ER -