Energy distribution of radial solutions to energy subcritical wave equation with an application on scattering theory

@article{Shen2018EnergyDO,
title={Energy distribution of radial solutions to energy subcritical wave equation with an application on scattering theory},
author={Ruipeng Shen},
journal={arXiv: Analysis of PDEs},
year={2018}
}
• Ruipeng Shen
• Published 27 August 2018
• Mathematics
• arXiv: Analysis of PDEs
The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space ($3\leq p<5$) whose initial data are radial and come with a finite energy. We split the energy into inward and outward energies, then apply energy flux formula to obtain the following asymptotic distribution of energy: Unless the solution scatters, its energy can be divided into two parts: "scattering energy" which concentrates around…
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