{"title":"广义薛定谔映射热流的等价形式及其演化","authors":"Penghong, Zhong","doi":"10.12988/nade.2015.536","DOIUrl":null,"url":null,"abstract":"We present a study of the singular and smooth solutions of the generalized Schrödinger map heat flow equation (GSMF) on hyperbolic space. Considering the associated hyperbolic Landau-Lifshitz spin evolution equation with uniaxial anisotropy together with applied field, we study the dynamics in terms of the stereographic variable. Firstly, a equivalent equation of this system is obtained. Based on this equivalent equation, we construct some singular and smooth solution of GSMF in 2-dimensional H2 space. We study these norm −1 solutions that allow us depict the mechanism of the evolution. Mathematics Subject Classification: 35K10, 35K65, 35Q40, 35Q55","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The equivalent form and the evolution of generalized Schrodinger map heat flow\",\"authors\":\"Penghong, Zhong\",\"doi\":\"10.12988/nade.2015.536\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a study of the singular and smooth solutions of the generalized Schrödinger map heat flow equation (GSMF) on hyperbolic space. Considering the associated hyperbolic Landau-Lifshitz spin evolution equation with uniaxial anisotropy together with applied field, we study the dynamics in terms of the stereographic variable. Firstly, a equivalent equation of this system is obtained. Based on this equivalent equation, we construct some singular and smooth solution of GSMF in 2-dimensional H2 space. We study these norm −1 solutions that allow us depict the mechanism of the evolution. Mathematics Subject Classification: 35K10, 35K65, 35Q40, 35Q55\",\"PeriodicalId\":315586,\"journal\":{\"name\":\"Nonlinear Analysis and Differential Equations\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis and Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/nade.2015.536\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis and Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/nade.2015.536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The equivalent form and the evolution of generalized Schrodinger map heat flow
We present a study of the singular and smooth solutions of the generalized Schrödinger map heat flow equation (GSMF) on hyperbolic space. Considering the associated hyperbolic Landau-Lifshitz spin evolution equation with uniaxial anisotropy together with applied field, we study the dynamics in terms of the stereographic variable. Firstly, a equivalent equation of this system is obtained. Based on this equivalent equation, we construct some singular and smooth solution of GSMF in 2-dimensional H2 space. We study these norm −1 solutions that allow us depict the mechanism of the evolution. Mathematics Subject Classification: 35K10, 35K65, 35Q40, 35Q55
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