The influence of oscillations on global existence for a class of semi-linear wave equations

摘要

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u tt-a(t)~2Δu=u_t~2-a(t) ~2|?u|~2. In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions.