{"title":"非经典扩散方程强拓扑空间中的指数吸引子","authors":"Liu Zhuan-lin","doi":"10.3724/SP.J.1160.2013.00285","DOIUrl":null,"url":null,"abstract":"In this article,we study the existence of exponential attractors in the strong topology space H~2(Ω) n H_0~1(Ω) for the nonclassical Diffusion Equation u_t — △_ut- △_u = f(u) + g(x) with critical exponent.In particular,after proving the existence of exponential attractors,we know that the global attractor in the strong topology space in[7,12,14]with finiteness of fractal dimension.","PeriodicalId":62008,"journal":{"name":"应用泛函分析学报","volume":"61 19 1","pages":"285"},"PeriodicalIF":0.0000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exponential Attractors in Strong Topology Space for a Nonclassical Diffusion Equation\",\"authors\":\"Liu Zhuan-lin\",\"doi\":\"10.3724/SP.J.1160.2013.00285\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article,we study the existence of exponential attractors in the strong topology space H~2(Ω) n H_0~1(Ω) for the nonclassical Diffusion Equation u_t — △_ut- △_u = f(u) + g(x) with critical exponent.In particular,after proving the existence of exponential attractors,we know that the global attractor in the strong topology space in[7,12,14]with finiteness of fractal dimension.\",\"PeriodicalId\":62008,\"journal\":{\"name\":\"应用泛函分析学报\",\"volume\":\"61 19 1\",\"pages\":\"285\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"应用泛函分析学报\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.3724/SP.J.1160.2013.00285\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用泛函分析学报","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.3724/SP.J.1160.2013.00285","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了具有临界指数的非经典扩散方程u_t -△_ut-△_u = f(u) + g(x)在强拓扑空间H~2(Ω) n H_0~1(Ω)中指数吸引子的存在性。特别地，在证明了指数吸引子的存在性之后，我们知道在强拓扑空间[7,12,14]中具有分形维数有限的全局吸引子。
Exponential Attractors in Strong Topology Space for a Nonclassical Diffusion Equation
In this article,we study the existence of exponential attractors in the strong topology space H~2(Ω) n H_0~1(Ω) for the nonclassical Diffusion Equation u_t — △_ut- △_u = f(u) + g(x) with critical exponent.In particular,after proving the existence of exponential attractors,we know that the global attractor in the strong topology space in[7,12,14]with finiteness of fractal dimension.
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