{"title":"描述光纤铺设过程模型的指数收敛到平衡速率","authors":"J. Dolbeault, A. Klar, C. Mouhot, C. Schmeiser","doi":"10.1093/amrx/abs015","DOIUrl":null,"url":null,"abstract":"This paper is devoted to the adaptation of the method developed in [4,3] to a Fokker-Planck equation for fiber lay-down which has been studied in [1,5]. Exponential convergence towards a unique stationary state is proved in a norm which is equivalent to a weighted $L^2$ norm. The method is based on a micro / macro decomposition which is well adapted to the diffusion limit regime.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"52 1","pages":"165-175"},"PeriodicalIF":0.0000,"publicationDate":"2012-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"47","resultStr":"{\"title\":\"Exponential Rate of Convergence to Equilibrium for a Model Describing Fiber Lay-Down Processes\",\"authors\":\"J. Dolbeault, A. Klar, C. Mouhot, C. Schmeiser\",\"doi\":\"10.1093/amrx/abs015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to the adaptation of the method developed in [4,3] to a Fokker-Planck equation for fiber lay-down which has been studied in [1,5]. Exponential convergence towards a unique stationary state is proved in a norm which is equivalent to a weighted $L^2$ norm. The method is based on a micro / macro decomposition which is well adapted to the diffusion limit regime.\",\"PeriodicalId\":89656,\"journal\":{\"name\":\"Applied mathematics research express : AMRX\",\"volume\":\"52 1\",\"pages\":\"165-175\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"47\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied mathematics research express : AMRX\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/amrx/abs015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied mathematics research express : AMRX","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/amrx/abs015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exponential Rate of Convergence to Equilibrium for a Model Describing Fiber Lay-Down Processes
This paper is devoted to the adaptation of the method developed in [4,3] to a Fokker-Planck equation for fiber lay-down which has been studied in [1,5]. Exponential convergence towards a unique stationary state is proved in a norm which is equivalent to a weighted $L^2$ norm. The method is based on a micro / macro decomposition which is well adapted to the diffusion limit regime.
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