Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (3): 373-383.
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CHEN Han-Lin, DAI Zheng-De
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Abstract:
文［１］中证明了耗散Ｚａｋｈａｒｏｖ方程组的最大吸引子的存在性．该文采用算子分解技术和构造犎２×犎１×犔２（犚）中渐进紧不变集的方法，得到了一维无界区域上耗散Ｚａｋｈａｒｏｖ方程组柯西问题的指数吸引子．
Key words: 耗散Ｚａｋｈａｒｏｖ方程组, 算子分解, 挤压性, 指数吸引子
CLC Number:
CHEN Han-Lin, DAI Zheng-De. Exponential Attrctor of the Cauchy Problem of Disspative Zakharov Equation in R[J].Acta mathematica scientia,Series A, 2001, 21(3): 373-383.
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１ ＹｏｎｇｓｈｅｎｇＬｉ，ＢｏｌｉｎｇＧｕｏ．ＡｔｔｒａｃｔｏｒｆｏｒｄｉｓｓｉｐａｔｉｖｅＺａｋｈａｒｏｖｅｑｕａｔｉｏｎｓｉｎａｎｕｎｂｏｕｎｄｅｄｄｏｍａｉｎ．Ｒｅｖｉｅｗｓｉｎ Ｍａｔｈ Ｐｈｙ，１９９７，９（６）：６７５－６８７ ２ ＢａｂｉｎＡ Ｖ，ＮｉｃｏｌａｅｎｋｏＢ．ＥｘｐｏｎｅｎｔｉａｌａｔｔｒａｃｔｏｒｏｆＲｅａｃｔｉｏｎＤｉｆｆｕｓｉｏｎｓｙｓｔｅｍｓｉｎａｎｕｎｂｏｕｎｄｅｄｄｏｍａｉｎ．ＪｏｆＤｙｎａｎｉｃｓ ａｎｄＤｉｆｆＥｑｓ，１９９５，７（４）：５６７－５８９ ３ ＦｌａｈａｕｔＩ．ＡｔｔｒａｃｔｏｒｓｆｏｒｔｈｅｄｉｓｓｉｐａｔｉｖｅＺａｋｈａｒｏｖｓｙｓｔｅｍ．ＮｏｎｌｉｎｅａｒＡｎａｌｙｓｉｓ，ＴＭＡ，１９９１，１６（７／８）：５９９－６３３ ４ ＢａｂｉｎＡ Ｖ，Ｖｉｓｈｉｋ ＭＩ．Ａｔｔｒａｃｔｏｒｓｏｆｐａｒｔｉａｌｄｉｆｆｅｒｎｔｉａｌｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎｓｉｎｕｎｂｏｕｎｄｅｄｄｏｍａｉｎ．ＰｒｏｃＲＳｏｃＥｄｉｎ ｂｕｒｇｈ，１９９０，１１６犃：２２１－２４３ ５ ＺｈｅｎｇｄｅＤａｉ，ＢｏｌｉｎｇＧｕｏ．ＩｎｅｒｔｉａｌｆｒａｃｔａｌｓｅｔｓｆｏｒｄｉｓｓｉｐａｔｉｖｅＺａｋｈａｒｏｖｓｙｓｔｅｍ．ＡｃｔａＭａｔｈＡｐｐｌＳｉｎｉｃａ，１９９７，１３（３）： ２７９－２８８ ６ ＺａｋｈａｒｏｖＶＥ．Ｃｏｌｌａｐｓｅｏｆｌａｎｇｍｕｉｒｗａｖｅｓ．ＳｏｖＰｈｙｓＪＥＴＰ，１９７２，３５：９０８－９１４ ７ ＢｏｌｉｎｇＧｕｏ，ＬｏｎｇｊｕｎＳｈｅｎｇ．Ｔｈｅｇｌｏｂａｌｅｘｉｓｔｅｎｃｅａｎｄｕｎｉｑｕｅｎｅｓｓｏｆｃｌａｓｓｉｃｓｏｌｕｔｉｏｎｏｎｔｈｅｐｅｒｉｏｄｉｃｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂ ｌｅｍＺａｋｈａｒｏｖｅｑｕａｔｉｏｎｓ．ＡｃｔａＭａｔｈＡｐｐｌＳｉｎｉｃａ，１９８２，５（３）：３１０－３２４ ８ ＹｏｎｇｓｈｅｎｇＬｉ．ＯｎｉｎｉｔｉａｌｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｆｏｒｔｗｏｄｉｍｅｎｓｉｏｎａｌｓｙｓｔｅｍｓｏｆＺａｋｈａｒｏｖｅｑｕａｔｉｏｎｓａｎｄｃｏｍｐｌｅｘ Ｓｃｈｒ¨ ｏｄｉｎｇｅｒＲｅａｌＢｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎｓ．ＪＰａｒｔｉａｌＤｉｆｆＥｑｓ，１９９２，５（２）：８１－９３ ９ ＫｅｎｉｇＣＥ，ＰｏｎｃｅＧ，ＶｅｇａＬ．ＯｎｔｈｅＺａｋｈａｒｏｖａｎｄＺａｋｈａｒｏｖＳｃｈｕｌｍａｎｓｙｓｔｅｍｓ．ＪＦｕｎｃｔＡｎａｌ，１９９５，１２７：２０４－２３４
Cited
An Inexact Alternating Direction Method for Solving a Class of Monotone Variational Inequalities