Asymptotics from scaling for nonlinear wave equations

Abstract

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the late-time behavior of solutions of the nonlinear problem in timelike and null directions.

14 pages; minor changes (notation, typos)

References in corpus (3)

• Universality of global dynamics for the cubic wave equation
• Linear and nonlinear tails II: exact decay rates in spherical symmetry
• Linear and nonlinear tails I: general results and perturbation theory