Asymptotic properties of solutions to dispersive equation of Schrödinger type

• Hayashi Nakao

  Department of Mathematics, Graduate School of Science, Osaka University

• Naumkin Pavel I.

  Instituto de Matemáticas, UNAM Campus Morelia

Bibliographic Information

Other Title

• Asymptotic properties of solutions to dispersive equation of Schrodinger type

Abstract

We find the asymptotic behavior for large time of solutions to the dispersive equations of Schrödinger type <br>u_t-$¥frac{i}{¥rho}$ |∂_x|^ρu = 0, (t,x) ∈ R × R,<br>where ρ ≥ 2. We obtain some estimates of solutions of linear problem and apply them to nonlinear problems with power nonlinearities of order p ≥ 3. The nonexistence of wave operator and existence of the modified wave operator for the critical nonlinearity i λ |u|²u are studied.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 60 (3), 631-652, 2008

  The Mathematical Society of Japan

Keywords

• asymptotics of solutions
• dispersive equations
• nonlinear problems

Details

• CRID: 1390001205114695168
• NII Article ID: 10024331840
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06030631
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 9582966
• Web Site: http://id.ndl.go.jp/bib/9582966
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9582966
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed