Large time behavior of solutions to Schrodinger equations with a dissipative nonlinearity for arbitrarily large initial data

• Kita Naoyasu

  Faculty of Education and Culture University of Miyazaki Gakuen-Kibanadai Nishi

• Shimomura Akihiro

  Department of Mathematics and Information Sciences Tokyo Metropolitan University

書誌事項

タイトル別名

• Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data
• <em>Large time behavior of Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data</em>,
• Dedicated to Professor Kenji Yajima on his sixtieth birthday

抄録

We study the asymptotic behavior in time of solutions to the Cauchy problem of nonlinear Schrödinger equations with a long-range dissipative nonlinearity given by λ |u|^p-1u in one space dimension, where 1 < p ≤ 3 (namely, p is a critical or subcritical exponent) and λ is a complex constant satisfying Im λ < 0 and ((p-1)/2√p) |Re λ| ≤ |Im λ|. We present the time decay estimates and the large-time asymptotics of the solution for arbitrarily large initial data, when “p = 3” or &ladquo;p < 3 and p is suitably close to 3”.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 61 (1), 39-64, 2009

  一般社団法人 日本数学会

キーワード

• nonlinear Schrödinger equation
• asymptotic behavior for large data
• dissipative nonlinearity
• critical or subcritical nonlinearity

詳細情報

• CRID: 1390282680091389056
• NII論文ID: 10024905488
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06110039
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 9773255
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9773255
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可