Geodesic
On the real analyticity of the scattering operator for the Hartree equation
Changxing Miao1 ; Haigen Wu2 ; Junyong Zhang3
1 Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing, China, 100088
2 The Graduate School of China Academy of Engineering Physics P.O. Box 2101 Beijing, China, 100088 and School of Mathematics and Information Science Henan Polytechnic University Jiaozuo, China, 454000
3 The Graduate School of China Academy of Engineering Physics P.O. Box 2101 Beijing, China, 100088
Annales Polonici Mathematici, Tome 95 (2009) no. 3, pp. 227-242

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

\def\barDelta{{\mit\Delta}}We study the real analyticity of the scattering operator for the Hartree equation $ i\partial _tu=-{\mit\Delta} u+u(V*|u|^2)$. To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome dif{f}iculties which arise from absence of good properties as for the Klein–Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the nonlinear Klein–Gordon equation with cubic nonlinearity.
DOI : 10.4064/ap95-3-3
Keywords: def bardelta mit delta study real analyticity scattering operator hartree equation partial mit delta v* end exploit interior exterior cut off time space together compactness argument overcome dif iculties which arise absence properties klein gordon equation finite speed propagation ideal time decay estimate additionally method paper allows simplify proof analyticity scattering operator nonlinear klein gordon equation cubic nonlinearity

Changxing Miao 1 ; Haigen Wu 2 ; Junyong Zhang 3

1 Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing, China, 100088
2 The Graduate School of China Academy of Engineering Physics P.O. Box 2101 Beijing, China, 100088 and School of Mathematics and Information Science Henan Polytechnic University Jiaozuo, China, 454000
3 The Graduate School of China Academy of Engineering Physics P.O. Box 2101 Beijing, China, 100088 
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Changxing Miao; Haigen Wu; Junyong Zhang. On the real analyticity of the scattering operator
 for the Hartree equation. Annales Polonici Mathematici, Tome 95 (2009) no. 3, pp. 227-242. doi: 10.4064/ap95-3-3

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