{"title":"一个受癌细胞影响的趋化系统的存在性和独特性","authors":"Gang Li, Huijuan Hu, Xi Chen, Feijun Jiang","doi":"10.12691/IJPDEA-7-1-1","DOIUrl":null,"url":null,"abstract":"We present a mathematical analysis of a reaction-diffusion model in a bounded open domain which describes vascular endothelial growth factor(VEGF), endothelial cells and oxygen. We use the parabolic theory to prove the existence of the solution in the function space under the homogeneous Neumann conditions. Then we get the existence of nonnegative solution in by using the global Schauder estimation.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"16 1","pages":"1-7"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and Uniqueness of a Chemotaxis System Influenced by Cancer Cells\",\"authors\":\"Gang Li, Huijuan Hu, Xi Chen, Feijun Jiang\",\"doi\":\"10.12691/IJPDEA-7-1-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a mathematical analysis of a reaction-diffusion model in a bounded open domain which describes vascular endothelial growth factor(VEGF), endothelial cells and oxygen. We use the parabolic theory to prove the existence of the solution in the function space under the homogeneous Neumann conditions. Then we get the existence of nonnegative solution in by using the global Schauder estimation.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"16 1\",\"pages\":\"1-7\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12691/IJPDEA-7-1-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12691/IJPDEA-7-1-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence and Uniqueness of a Chemotaxis System Influenced by Cancer Cells
We present a mathematical analysis of a reaction-diffusion model in a bounded open domain which describes vascular endothelial growth factor(VEGF), endothelial cells and oxygen. We use the parabolic theory to prove the existence of the solution in the function space under the homogeneous Neumann conditions. Then we get the existence of nonnegative solution in by using the global Schauder estimation.
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