Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly

Details Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly

2011-08-06

arxiv.org/abs/1108.1450v1

Mathematics

Analysis of PDEs

22pages

Scientific paper

We consider inverse scattering problems for the three-dimensional Hartree equation. We prove that if the unknown interaction potential $V(x)$ of the equation satisfies some rapid decay condition, then we can uniquely determine the exact value of $\partial_\xi^\alpha \hat{V}(0)$ for any multi-index $\alpha$ by the knowledge of the scattering operator for the equation. Furthermore, we show some stability estimate for identifying $\partial_\xi^\alpha \hat{V}(0)$.

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