{"title":"带对流项的随机退化抛物方程的零可控性","authors":"Lin Yan, Bin Wu","doi":"10.1002/mma.10686","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This paper concerns the null controllability of stochastic degenerate parabolic equation with convection term in weakly degenerate case. Due to the degeneracy, we first transfer to study an approximate nondegenerate system. Next, we establish the Carleman estimate for backward stochastic degenerate parabolic equation with convection term. In order to deal with the convection term, the Carleman estimate is established by introducing an auxiliary function to transfer the diffusion and the convection term into a whole complex divergence-like form. By this Carleman estimate, we then obtain an observability inequality for the adjoint system of the approximate system. Based on the observability inequality and an approximate argument, we proved our null controllability result.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6495-6505"},"PeriodicalIF":2.1000,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Null Controllability of Stochastic Degenerate Parabolic Equation With Convection Term\",\"authors\":\"Lin Yan, Bin Wu\",\"doi\":\"10.1002/mma.10686\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>This paper concerns the null controllability of stochastic degenerate parabolic equation with convection term in weakly degenerate case. Due to the degeneracy, we first transfer to study an approximate nondegenerate system. Next, we establish the Carleman estimate for backward stochastic degenerate parabolic equation with convection term. In order to deal with the convection term, the Carleman estimate is established by introducing an auxiliary function to transfer the diffusion and the convection term into a whole complex divergence-like form. By this Carleman estimate, we then obtain an observability inequality for the adjoint system of the approximate system. Based on the observability inequality and an approximate argument, we proved our null controllability result.</p>\\n </div>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 6\",\"pages\":\"6495-6505\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.10686\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10686","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Null Controllability of Stochastic Degenerate Parabolic Equation With Convection Term
This paper concerns the null controllability of stochastic degenerate parabolic equation with convection term in weakly degenerate case. Due to the degeneracy, we first transfer to study an approximate nondegenerate system. Next, we establish the Carleman estimate for backward stochastic degenerate parabolic equation with convection term. In order to deal with the convection term, the Carleman estimate is established by introducing an auxiliary function to transfer the diffusion and the convection term into a whole complex divergence-like form. By this Carleman estimate, we then obtain an observability inequality for the adjoint system of the approximate system. Based on the observability inequality and an approximate argument, we proved our null controllability result.
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Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
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