TY - JOUR
T1 - Scattering for Semilinear Wave Equation with Small Data in High Space Dimensions
JO - Journal of Partial Differential Equations
VL - 1
SP - 26
EP - 40
PY - 1999
DA - 1999/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5522.html
KW - Semilinear wave equation
KW - scattering
KW - asymptotic behavior
AB -  In this paper we study the scattering theory for the semilincar wave equation u_{tt} - Δu = F(u(t, x), Du(t, x)) in R^n (n ≥ 4) with smooth and small data. We show that the scattering operator exists for the nonlinear term F = F(λ) = O(|λ|^{1, α}), where α is an integer and satisfies α ≥ 2, n = 4; α ≥ I, n ≥ 5.