{"title":"Exact solutions of Diffusion Equation on sphere","authors":"Yadollah AryaNejad","doi":"10.22034/CMDE.2021.44459.1876","DOIUrl":null,"url":null,"abstract":"We examine the diffusion equation on the sphere. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. We prove for one-dimensional optimal systems of Eq.(4), space is expanding Ricci solitons. Reductions of similarities related to subalgebras are classified, and some exact invariant solutions of the diffusion equation on the sphere are presented.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2021.44459.1876","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We examine the diffusion equation on the sphere. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. We prove for one-dimensional optimal systems of Eq.(4), space is expanding Ricci solitons. Reductions of similarities related to subalgebras are classified, and some exact invariant solutions of the diffusion equation on the sphere are presented.
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