{"title":"退化噪声驱动下Kuramoto-Sivashinsky方程的不可约性","authors":"Peng Gao","doi":"10.1051/cocv/2022014","DOIUrl":null,"url":null,"abstract":"In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number of Fourier modes. In order to obtain the irreducibility,\n\nwe first investigate the approximate controllability of Kuramoto-Sivashinsky equation driven by a finite-dimensional force, the proof is based on Agrachev-Sarychev type geometric control approach.\n\nNext, we study the continuity of solving operator for deterministic Kuramoto-Sivashinsky equation. Finally, combining the approximate controllability with continuity of solving operator,\n\nwe establish the irreducibility of Kuramoto-Sivashinsky equation.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":"228 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise\",\"authors\":\"Peng Gao\",\"doi\":\"10.1051/cocv/2022014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number of Fourier modes. In order to obtain the irreducibility,\\n\\nwe first investigate the approximate controllability of Kuramoto-Sivashinsky equation driven by a finite-dimensional force, the proof is based on Agrachev-Sarychev type geometric control approach.\\n\\nNext, we study the continuity of solving operator for deterministic Kuramoto-Sivashinsky equation. Finally, combining the approximate controllability with continuity of solving operator,\\n\\nwe establish the irreducibility of Kuramoto-Sivashinsky equation.\",\"PeriodicalId\":50500,\"journal\":{\"name\":\"Esaim-Control Optimisation and Calculus of Variations\",\"volume\":\"228 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Control Optimisation and Calculus of Variations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/cocv/2022014\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Control Optimisation and Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/cocv/2022014","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise
In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number of Fourier modes. In order to obtain the irreducibility,
we first investigate the approximate controllability of Kuramoto-Sivashinsky equation driven by a finite-dimensional force, the proof is based on Agrachev-Sarychev type geometric control approach.
Next, we study the continuity of solving operator for deterministic Kuramoto-Sivashinsky equation. Finally, combining the approximate controllability with continuity of solving operator,
we establish the irreducibility of Kuramoto-Sivashinsky equation.
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ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations.
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in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.
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