Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms

• Sunagawa Hideaki

  Institute of Mathematics, University of Tsukuba

抄録

We consider the Cauchy problem for ∂_t²u-∂_x²u+u = -g(∂_tu)³ on the real line. It is shown that if g>0, the solution has an additional logarithmic time decay in comparison with the free evolution in the sense of L^p, 2≤p≤∞. Moreover, the asymptotic profile of u(t,x) as t→+∞ is obtained. We also discuss a generalization. Consequently we see that the “null condition” in the sense of J.-M. Delort (Ann. Sci. École Norm. Sup., 34 (2001), 1-61) is not optimal for small data global existence for nonlinear Klein-Gordon equations.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 58 (2), 379-400, 2006

  一般社団法人 日本数学会

キーワード

• Klein-Gordon equation
• nonlinear dissipation
• large time asymptotics
• null condition

詳細情報

• CRID: 1390001205116522368
• NII論文ID: 10018381270
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1149166781
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2228565
• NDL書誌ID: 7892106
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7892106
• 本文言語コード: en
• データソース種別:
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  • NDL
  • Crossref
  • CiNii Articles
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