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| EXISTENCE TIME FOR THE SEMILINEAR SCHR?DINGER EQUATION | |
| 作者姓名： | Wei MingjunDept. of Math. Zhejiang Univ. Hangzhou China. |
| 作者单位： | Wei MingjunDept. of Math.，Zhejiang Univ.，Hangzhou 310027，China. |
| 摘 要： | § 1 ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ ,ｗｅｗｉｌｌｃｏｎｓｉｄｅｒｔｈｅｓｅｍｉｌｉｎｅａｒＳｃｈｒ ｄｉｎｇｅｒｅｑｕａｔｉｏｎｉｎｏｎｅｓｐａｃｅｄｉｍｅｎｓｉｏｎｏｆｔｈｅｔｙｐｅｕｔ-ｉｕｘｘ =Ｆ(ｕ) . (ｘ ,ｔ)∈Ｒ×Ｒ+,( 1 )ｕ(ｘ ,0 ) =ｕ0 , ｘ ∈Ｒ ,( 2 )ｗｈｅｒｅｕ =ｕ(ｘ ,ｔ)ｉｓｃｏｍｐｌｅｘ ｖａｌｕｅｄｆｕｎｃｔｉｏｎ ,ａｎｄＦｉｓａｓｍｏｏｔｈｆｕｎｃｔｉｏｎｏｆｕｓｕｃｈｔｈａｔ｜Ｆ(ｕ) ｜ =Ｏ( ｜ｕ｜α+1)ｆｏｒ |ｕ|ｓｕｆｆｉｃｉｅｎｔｌｙｓｍａｌｌａｎｄ… |
| 关 键 词： | semilinear Schrdinger equation existence time Sobolev embedding. |
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