{"title":"Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions","authors":"Farid Nouioua, Bilal Basti","doi":"10.2478/aupcsm-2021-0003","DOIUrl":null,"url":null,"abstract":"Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"12 1","pages":"43 - 56"},"PeriodicalIF":0.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/aupcsm-2021-0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.
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