A. Kovtanyuk, A. Chebotarev, Anastasiya A. Dekalchuk, N. Botkin, R. Lampe
{"title":"An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain","authors":"A. Kovtanyuk, A. Chebotarev, Anastasiya A. Dekalchuk, N. Botkin, R. Lampe","doi":"10.1109/DD46733.2019.9016443","DOIUrl":null,"url":null,"abstract":"A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 Days on Diffraction (DD)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DD46733.2019.9016443","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.
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