On space-time means and strong global solutions of nonlinear hyperbolic equations

Abstract

On demontre l'existence de solutions globales appartenant a L ∞ loc (R 2 ; L 2 2 (R n )) pour des equations non lineaires de la forme: ∂ t u=Δu+b(x,D)u+f(u)=0, (t,x)∈R + ×R n , u(0,x)=φ 0 (x), ∂ t u(0,x)=φ 1 (x), x∈R n