{"title":"带有广义平流项的平流扩散方程：拟合优度分析与实例","authors":"Tetyana Malysheva , Luther W. White","doi":"10.1016/j.exco.2024.100159","DOIUrl":null,"url":null,"abstract":"<div><div>We consider a Cauchy–Dirichlet problem for a semilinear advection–diffusion equation with a generalized advection term. Specific examples include an incision–diffusion landscape evolution model and a viscous Hamilton–Jacobi equation with an absorbing gradient term. We establish existence and uniqueness of a weak solution and its continuous dependence on initial data and a source term.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"6 ","pages":"Article 100159"},"PeriodicalIF":0.0000,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An advection–diffusion equation with a generalized advection term: Well-posedness analysis and examples\",\"authors\":\"Tetyana Malysheva , Luther W. White\",\"doi\":\"10.1016/j.exco.2024.100159\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider a Cauchy–Dirichlet problem for a semilinear advection–diffusion equation with a generalized advection term. Specific examples include an incision–diffusion landscape evolution model and a viscous Hamilton–Jacobi equation with an absorbing gradient term. We establish existence and uniqueness of a weak solution and its continuous dependence on initial data and a source term.</div></div>\",\"PeriodicalId\":100517,\"journal\":{\"name\":\"Examples and Counterexamples\",\"volume\":\"6 \",\"pages\":\"Article 100159\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Examples and Counterexamples\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666657X24000259\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X24000259","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An advection–diffusion equation with a generalized advection term: Well-posedness analysis and examples
We consider a Cauchy–Dirichlet problem for a semilinear advection–diffusion equation with a generalized advection term. Specific examples include an incision–diffusion landscape evolution model and a viscous Hamilton–Jacobi equation with an absorbing gradient term. We establish existence and uniqueness of a weak solution and its continuous dependence on initial data and a source term.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
