{"title":"关于轴对称扩散方程的注解","authors":"A. Patkowski","doi":"10.1017/S1446181121000110","DOIUrl":null,"url":null,"abstract":"Abstract We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for \n$u(r,t)$\n as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"58 1","pages":"333 - 341"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A NOTE ON THE AXISYMMETRIC DIFFUSION EQUATION\",\"authors\":\"A. Patkowski\",\"doi\":\"10.1017/S1446181121000110\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for \\n$u(r,t)$\\n as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.\",\"PeriodicalId\":74944,\"journal\":{\"name\":\"The ANZIAM journal\",\"volume\":\"58 1\",\"pages\":\"333 - 341\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The ANZIAM journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/S1446181121000110\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The ANZIAM journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/S1446181121000110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for
$u(r,t)$
as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.
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