Asymptotic energy distribution of one-dimensional nonlinear wave equation

Ruipeng Shen

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arXiv · 2008.03037

Asymptotic energy distribution of one-dimensional nonlinear wave equation

Ruipeng Shen

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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.

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Ruipeng Shen. 2020-08-07. Asymptotic energy distribution of one-dimensional nonlinear wave equation. https://arxiv.org/abs/2008.03037

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