On small data scattering with cubic convolution nonlinearity

Kiyoshi MOCHIZUKI

doi:10.2969/jmsj/04110143

Kiyoshi MOCHIZUKI

著者情報

ジャーナルフリー

1989 年 41 巻 1 号 p. 143-160

DOI https://doi.org/10.2969/jmsj/04110143

詳細

Published: 1989 Received: 1987/09/07 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Takeyuki Hida on his sixtieth birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. Bergh and J. Löfström, Interpolation Spaces, Springer, 1976.
2) Ph. Brenner, On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, J. Differential Equations, 56 (1985), 310-344.
3) J. P. Dias and M. Figueira, Conservation laws and time decay of some nonlinear Schrödinger-Hartree equations and systems, J. Math. Anal. Appl., 84 (1981), 486-508.
4) J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Z., 170 (1980), 109-136.
5) R. T. Glassey, Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations, Comm. Math. Phys., 53 (1977), 9-18.
6) E. Gross, Quantum theory of interacting bosons, Ann. Physics, 9 (1960), 292-324.
7) N. Hayashi and Y. Tsutsumi, Scattering theory for Hartree type equations, Ann. Inst. H. Poincaré, Phys. Théor., 46 (1987), 187-213.
8) N. Hayashi and T. Ozawa, Scattering theory in the weighted L²(Rⁿ) spaces for some Schrödinger equations, preprint, 1987.
9) L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983.
10) P. L. Lions, The Choquard equation and related equations, J. Nonlinear Anal. Theory, Methods, Appl., 4 (1980), 1073-1079.
11) S. Matsumoto and K. Mochizuki, On blowing up of solutions of Schrödinger equations with cubic convolution, preprint, 1987.
12) G. P. Menzala, On regular solutions of a nonlinear equations of Choquard's type, Proc. Roy. Soc. Edinburgh, Sect. A, 86 (1980), 291-301.
13) G. P. Menzala and W. A. Strauss, On a wave equation with cubic convolution, J. Differential Equations, 43 (1982), 93-105.
14) K. Mochizuki and T. Motai, On small data scattering for some nonlinear wave equations, Patterns and Waves-Qualitative Analysis of Nonlinear Differential Equations-, 1986, pp. 543-560.
15) H. Pecher, L^p-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I, Math. Z., 150 (1976), 159-183.
16) H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z., 185 (1984), 261-270.
17) W. A. Strauss, Nonlinear scattering theory at law energy, J. Funct. Anal., 41 (1981), 110-133, Sequel, 43 (1981), 281-293.

Right : [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, 1976.
[2] Ph. Brenner, On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, J. Differential Equations, 56 (1985), 310-344.
[3] J. P. Dias and M. Figueira, Conservation laws and time decay of some nonlinear Schrödinger-Hartree equations and systems, J. Math. Anal. Appl., 84 (1981), 486-508.
[4] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Z., 170 (1980), 109-136.
[5] R. T. Glassey, Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations, Comm. Math. Phys., 53 (1977), 9-18.
[6] E. Gross, Quantum theory of interacting bosons, Ann. Physics, 9 (1960), 292-324.
[7] N. Hayashi and Y. Tsutsumi, Scattering theory for Hartree type equations, Ann. Inst. H. Poincaré, Phys. Théor., 46 (1987), 187-213.
[8] N. Hayashi and T. Ozawa, Scattering theory in the weighted L²(Rⁿ) spaces for some Schrödinger equations, preprint, 1987.
[9] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983.
[10] P. L. Lions, The Choquard equation and related equations, J. Nonlinear Anal. Theory, Methods, Appl., 4 (1980), 1073-1079.
[11] S. Matsumoto and K. Mochizuki, On blowing up of solutions of Schrödinger equations with cubic convolution, preprint, 1987.
[12] G. P. Menzala, On regular solutions of a nonlinear equations of Choquard's type, Proc. Roy. Soc. Edinburgh, Sect. A, 86 (1980), 291-301.
[13] G. P. Menzala and W. A. Strauss, On a wave equation with cubic convolution, J. Differential Equations, 43 (1982), 93-105.
[14] K. Mochizuki and T. Motai, On small data scattering for some nonlinear wave equations, Patterns and Waves-Qualitative Analysis of Nonlinear Differential Equations-, 1986, pp. 543-560.
[15] H. Pecher, L^p-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I, Math. Z., 150 (1976), 159-183.
[16] H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z., 185 (1984), 261-270.
[17] W. A. Strauss, Nonlinear scattering theory at law energy, J. Funct. Anal., 41 (1981), 110-133, Sequel, 43 (1981), 281-293.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）