Scattering and self-similar solutions for the nonlinear wave equation

摘要

We study scattering theory and self-similar solutions for the nonlinear wave equations □u + λ|u|~(p-1) u = 0 in two or three space dimensions under the assumption p_0(n) < p < 1 + 4/(n - 1), where p_0(n) is the larger root of the equation (n - 1)p~2 - (n + 1)p - 2 = 0. The relation between the theory of scattering and that of self-similar solution is considered from the point of view of asymptotically free solutions and asymptotically self-similar solutions.