On the semirelativistic Hartree-type equation

Yonggeun Cho, Tohru Ozawa

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We study the global Cauchy problem and scattering problem for the semirelativistic Hartree-type equation in ℝn, n ≥ 1, with nonlocal nonlinearity F(u) = λ(|x| * |u| 2)u, 0 < γ < n. We prove the existence and uniqueness of global solutions for 0 < γ < 2n/n+1, n ≥ 2 or γ > 2, n ≥ 3, and the nonexistence of asymptotically-free solutions for 0 < γ ≤ 1, n ≥ 3. We also specify asymptotic behavior of solutions as the mass tends to zero and infinity.

Original languageEnglish
Pages (from-to)1060-1074
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number4
DOIs
Publication statusPublished - 2006 Dec 1
Externally publishedYes

Keywords

  • Global solution
  • Nonexistence of asymptotically free solutions
  • Scattering
  • Semirelativistic Hartree-type equation

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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