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On the semi-relativistic Hartree type equation
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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