Asymptotic energy distribution of one-dimensional nonlinear wave equation

Abstract

In this work we consider the defocusing nonlinear wave equation in one-dimensional space. We show that almost all energy is located near the light cone $|x|=|t|$ as time tends to infinity. We also prove that any light cone will eventually contain some energy. As an application we obtain a result about the asymptotic behaviour of solutions to focusing one-dimensional wave equation with compact-supported initial data.

18 pages, 4 figures

References in corpus (2)

• Inward/outward Energy Theory of Wave Equation in Higher Dimensions
• Inward/outward Energy Theory of Non-radial Solutions to 3D Semi-linear Wave Equation