TY - JOUR
T1 - Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
PY - 2008/1/1
Y1 - 2008/1/1
N2 - We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ, 1 with β = max (frac(3, 2), 1 + frac(2, n)) for the nonlinear Klein-Gordon equation with a power nonlinearityut t - Δ u + u = μ | u |σ - 1 u, (t, x) ∈ R × Rn, where 1 + frac(4, n + 2) < σ < 1 + frac(4, n) for n ≥ 3, μ ∈ C.
AB - We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ, 1 with β = max (frac(3, 2), 1 + frac(2, n)) for the nonlinear Klein-Gordon equation with a power nonlinearityut t - Δ u + u = μ | u |σ - 1 u, (t, x) ∈ R × Rn, where 1 + frac(4, n + 2) < σ < 1 + frac(4, n) for n ≥ 3, μ ∈ C.
KW - Asymptotics of solutions
KW - Higher space dimensions
KW - Nonlinear Klein-Gordon equations
KW - Power nonlinearities
KW - Scattering operator
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U2 - 10.1016/j.jde.2007.10.002
DO - 10.1016/j.jde.2007.10.002
M3 - Article
AN - SCOPUS:36048947313
SN - 0022-0396
VL - 244
SP - 188
EP - 199
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -