Conformal conservation law, time decay and scattering for nonlinear wave equations (Q1880934)

The author considers solutions of the Cauchy problem to the equation \[ u_{tt}-\triangle u+\lambda _1| u| ^{\rho _1-1}u+\lambda _2| u| ^{\rho _2-1}u=0, \qquad t\in \mathbb{R}, \;x\in \mathbb{R}^n\;(n=3\dots 7). \] He improves results of \textit{J. Ginibre} and \textit{G. Velo} [Ann. Inst. Henri Poincaré, Phys. Théor. 47, 221--261, 263--276 (1987; Zbl 0644.35067)] and deduces sharp estimates for asymptotic behavior of the solution to the problem.