On the real analyticity of the scattering operator for the Hartree equation

Tom 95 / 2009

Changxing Miao, Haigen Wu, Junyong Zhang Annales Polonici Mathematici 95 (2009), 227-242 MSC: 35P25, 35Q55. DOI: 10.4064/ap95-3-3

Streszczenie

\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.

Autorzy

  • Changxing MiaoInstitute of Applied Physics
    and Computational Mathematics
    P.O. Box 8009
    Beijing, China, 100088
    e-mail
  • Haigen WuThe 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
    e-mail
  • Junyong ZhangThe Graduate School of China Academy
    of Engineering Physics
    P.O. Box 2101
    Beijing, China, 100088
    e-mail

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