Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (4): 433-438.
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GUO Ding-Hui
Online:
Published:
Supported by:
国家自然科学基金资助项目
Abstract:
讨论层流理论中描述比重相近的层流间相互作用的方程组的广义方程组．通过引进一类函数空间和一系列先验估计，应用不动点原理，分别得到该类广义层流方程组的初值问题在H^s(R),s≥1的局部适定性．
Key words: 非线性方程组, 初值问题, 适定性, 先验估计．
CLC Number:
GUO Ding-Hui. Local Well-Posedness of Initial Value Problem for Generalized Wave Model[J].Acta mathematica scientia,Series A, 2001, 21(4): 433-438.
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１ ＧｅａｒＪＡ，Ｇｒｉｍｓｈａｗ Ｒ．Ｗｅａｋａｎｄｓｔｒｏｎｇｉｎｔｅｒａｃｔｉｏｎｓｂｅｔｗｅｅｎｉｎｔｅｒｎａｌｓｏｌｉｔａｒｙｗａｖｅｓ．ＳｔｕｄｉｅｓｉｎＡｐｐｌＭａｔｈ，１９８４， ７０：２３５－２５８ ２ ＧｅａｒＪＡ．Ｓｔｒｏｎｇｉｎｔｅｒａｃｔｉｏｎｓｂｅｔｗｅｅｎｓｏｌｉｔａｒｙ ｗａｖｅｓｂｅｌｏｎｇｉｎｇｔｏｄｉｆｆｅｒｅｎｔｉａｌｗａｖｅｍｏｄｅｌ．Ｓｔｕｄｉｅｓｉｎ ＡｐｐｌＭａｔｈ， １９８５，７２：９５－１２４ ３ ＡｌａｒｃｏｎＥ，ＡｎｇｕｌｏＪ，ＭｏｎｔｅｎｅｇｒｏＪＦ．Ｓｔａｂｉｌｉｔｙａｎｄｉｎｓｔａｂｉｌｉｔｙｏｆｓｏｌｉｔａｒｙ ｗａｖｅｓｆｏｒａｎｏｎｌｉｎｅａｒｄｉｓｐｅｒｓｉｖｅｓｙｓｔｅｍ． ＮｏｎｌｉｎｅａｒＡｎａｌ，１９９９，３６（Ｓｅｒ．Ａ：Ｔｈｅｏｒｙ Ｍｅｔｈｏｄｓ）（８）：１０１５－１０３５ ４ ＫｅｎｉｇＣＥ，ＰｏｎｃｅＧ，ＶｅｇａＬ．ＷｅｌｌｐｏｓｅｄｎｅｓｓｏｆｔｈｅｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｆｏｒｔｈｅＫｄＶｅｑｕａｔｉｏｎ．ＪＡｍｅｒＭａｔｈＳｏｃ， １９９１，４：３２３－３４７ ５ ＫｅｎｉｇＣＥ，ＰｏｎｃｅＧ，ＶｅｇａＬ．ＷｅｌｌｐｏｓｅｄｎｅｓｓａｎｄｓｃａｔｔｅｒｉｎｇｒｅｓｕｌｔｓｆｏｒｔｈｅｇｅｎｅｒａｌｉｚｅｄＫｄＶｅｑｕａｔｉｏｎｖｉａｔｈｅｃｏｎｔｒａｃ ｔｉｏｎｐｒｉｎｃｉｐｌｅ．ＣｏｍｍＰｕｒｅＡｐｐｌＭａｔｈ，１９９３，４６（４）：５２７－６２０ ６ Ｃｒａｉｇ Ｗ，ＧｏｏｄｍａｎＪ．ＬｉｎｅａｒｄｉｓｐｅｒｓｉｖｅｅｑｕａｔｉｏｎｓｏｆＡｉｒｙｔｙｐｅ．ＪＤｉｆｆＥｑｕ，１９９０，８７：３８－６７
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