• Corpus ID: 235658637

Energy distribution of solutions to defocusing semi-linear wave equation in higher dimensional space

@inproceedings{Li2021EnergyDO,
  title={Energy distribution of solutions to defocusing semi-linear wave equation in higher dimensional space},
  author={Liang Li and Ruipeng Shen},
  year={2021}
}

• Liang Li, Ruipeng Shen
• Published 26 June 2021
• Mathematics

The topic of this paper is a semi-linear, defocusing wave equation utt − ∆u = −|u| u in sub-conformal case in the higher dimensional space whose initial data are radical and come with a finite energy. We prove some decay estimates of the the solutions if initial data decay at a certain rate as the spatial variable tends to infinity. A combination of this property with a method of characteristic lines give a scattering result if the initial data satisfy Eκ (u0, u1) = ∫ Rd (|x| + 1) ( 1 2 |∇u0(x)| 2 + 1 2 |u1(x)| 2 + 1 p+ 1 |u0(x)| p+1 ) dx < +∞. Here κ = (2−d)p+(d+2) p+1 .