On the Asymptotic Behavior of Solutions of Semi-linear Wave Equations

Abstract

utt -Au + ut +/(«, ut, Vu) - 0 . We show the asymptotic properties of the solutions of the linear equation [(2) with /*=0] in 2. 1 and those of the nonlinear equation (2) in 2. 2 and 2. 3. Notation. We denote by U the space of measurable functions u on Rn whose ^>-th powers (l<r<Joo) are integrable with the norm 1/p U / f = vu(xy J