TY - JOUR
T1 - Global Existence of Small Solutions to Quadratic Nonlinear Wave Equations in an Exterior Domain
AU - Hayashi, Nakao
PY - 1995/8/1
Y1 - 1995/8/1
N2 - We consider the initial boundary value problem for the nonlinear wave equation [formula] where □ = ∂2t − ΔB = (x : |x| = [formula] > R), ∂B = (x : |x| = R), u0, u1 are real valued functions ϵ0 is a sufficiently small positive constant. In this paper it is shown that small solutions to (*) exist globally in time when n = 4. Our method in this paper is applicable to the more general nonlinear wave equations such that □u = F(∂tu, ∂t ∂u, ∂2tu), where F is a quadratic nonlinearity in (∂tu, part;t ∂u, ∂2tu), ∂ = (∂1, ∂2, … , ∂n) and n ≥ 4.
AB - We consider the initial boundary value problem for the nonlinear wave equation [formula] where □ = ∂2t − ΔB = (x : |x| = [formula] > R), ∂B = (x : |x| = R), u0, u1 are real valued functions ϵ0 is a sufficiently small positive constant. In this paper it is shown that small solutions to (*) exist globally in time when n = 4. Our method in this paper is applicable to the more general nonlinear wave equations such that □u = F(∂tu, ∂t ∂u, ∂2tu), where F is a quadratic nonlinearity in (∂tu, part;t ∂u, ∂2tu), ∂ = (∂1, ∂2, … , ∂n) and n ≥ 4.
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U2 - 10.1006/jfan.1995.1091
DO - 10.1006/jfan.1995.1091
M3 - Article
AN - SCOPUS:0000752929
VL - 131
SP - 302
EP - 344
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -