{"title":"表面活性剂在薄膜上扩散的退化系统的非负弱解","authors":"M. Chugunova, R. Taranets","doi":"10.1093/AMRX/ABS014","DOIUrl":null,"url":null,"abstract":"Depending on the parameter range, we prove local and global in time existence of nonnegative weak solutions to a coupled system of two degenerate parabolic equations. This system models the spreading of an insoluble surfactant on a thin liquid film. This model includes gravity, surface tension, capillarity effects, and van der Waals forces. The surface diffusion coefficient is not assumed constant and depends on the surfactant concentration.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"19 1","pages":"102-126"},"PeriodicalIF":0.0000,"publicationDate":"2012-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Nonnegative Weak Solutions for a Degenerate System Modeling the Spreading of Surfactant on Thin Films\",\"authors\":\"M. Chugunova, R. Taranets\",\"doi\":\"10.1093/AMRX/ABS014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Depending on the parameter range, we prove local and global in time existence of nonnegative weak solutions to a coupled system of two degenerate parabolic equations. This system models the spreading of an insoluble surfactant on a thin liquid film. This model includes gravity, surface tension, capillarity effects, and van der Waals forces. The surface diffusion coefficient is not assumed constant and depends on the surfactant concentration.\",\"PeriodicalId\":89656,\"journal\":{\"name\":\"Applied mathematics research express : AMRX\",\"volume\":\"19 1\",\"pages\":\"102-126\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied mathematics research express : AMRX\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/AMRX/ABS014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied mathematics research express : AMRX","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/AMRX/ABS014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Nonnegative Weak Solutions for a Degenerate System Modeling the Spreading of Surfactant on Thin Films
Depending on the parameter range, we prove local and global in time existence of nonnegative weak solutions to a coupled system of two degenerate parabolic equations. This system models the spreading of an insoluble surfactant on a thin liquid film. This model includes gravity, surface tension, capillarity effects, and van der Waals forces. The surface diffusion coefficient is not assumed constant and depends on the surfactant concentration.