# 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} }

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…

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