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On the semi-relativistic Hartree type equation

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83923

Title: On the semi-relativistic Hartree type equation
Authors: Cho, Yonggeun Browse this author
Ozawa, Tohru Browse this author
Keywords: semi-relativistic Hartree type equation
global solution
scattering
non-existence of asymptotically free solution
Issue Date: 2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 773
Start Page: 1
End Page: 16
Abstract: We study the global Cauchy problem and scattering problem for the semi-relativistic equation in $\mathbb{R}^n, n \ge 1$ with nonlocal nonlinearity $F(u) = \lambda (|x|^{-\gamma} * |u|^2)u, 0 <\gamma < n$. We prove the existence and uniqueness of global solutions for $0 < \gamma < \frac{2n}{n+1}, n \ge 2$ or $\gamma > 2, n \ge 3$ and the non-existence of asymptotically free solutions for $0 < \gamma \le 1, n\ge 3$. We also specify asymptotic behavior of solutions as the mass tends to zero and infinity.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69581
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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