On the semi-relativistic Hartree type equation

• Cho Yonggeun

• Ozawa Tohru

抄録

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.

収録刊行物

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 773 1-16, 2006

  Department of Mathematics, Hokkaido University

キーワード

• semi-relativistic Hartree type equation
• global solution
• scattering
• non-existence of asymptotically free solution

詳細情報

• CRID: 1390853649725496448
• NII論文ID: 120006459478
• DOI: 10.14943/83923
• HANDLE: 2115/69581
• 本文言語コード: en
• データソース種別:
  • JaLC
  • IRDB
  • CiNii Articles
• 抄録ライセンスフラグ: 使用可