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.
Journal
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- Hokkaido University Preprint Series in Mathematics
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Hokkaido University Preprint Series in Mathematics 773 1-16, 2006
Department of Mathematics, Hokkaido University
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Details
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- CRID
- 1390853649725496448
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- NII Article ID
- 120006459478
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- DOI
- 10.14943/83923
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- HANDLE
- 2115/69581
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- CiNii Articles
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- Abstract License Flag
- Allowed