TY - JOUR
T1 - Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data
AU - Zhou , Yi
JO - Journal of Partial Differential Equations
VL - 2
SP - 135
EP - 144
PY - 1995
DA - 1995/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5647.html
KW - Wave equation
KW - Cauchy problem
KW - global solution
AB - In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small.