A. Kovtanyuk, A. Chebotarev, Anastasiya A. Dekalchuk, N. Botkin, R. Lampe
{"title":"求解脑内氧输运初边值问题的迭代算法","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":"{\"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}","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}
An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
