{"title":"一维非均相反应扩散方程的控制问题","authors":"M. Sônego, R. Roychowdhury","doi":"10.3934/eect.2022035","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>We are concerned with the controllability of a general heterogeneous semilinear parabolic equation of the form <inline-formula><tex-math id=\"M1\">\\begin{document}$ y_t(x,t)=y_{xx}(x,t)+f(x,y(x,t)) $\\end{document}</tex-math></inline-formula> in one space dimension using boundary static controls. More precisely, we provide conditions so that, using only static controls at the boundary, a certain target (a steady-state of the equation) is reached in infinite time. Applications of the main result are also presented, in particular, we provide several controllability results to heterogeneous equations of monostable and bistable types.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"16 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on control of one-dimensional heterogeneous reaction-diffusion equations\",\"authors\":\"M. Sônego, R. Roychowdhury\",\"doi\":\"10.3934/eect.2022035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style='text-indent:20px;'>We are concerned with the controllability of a general heterogeneous semilinear parabolic equation of the form <inline-formula><tex-math id=\\\"M1\\\">\\\\begin{document}$ y_t(x,t)=y_{xx}(x,t)+f(x,y(x,t)) $\\\\end{document}</tex-math></inline-formula> in one space dimension using boundary static controls. More precisely, we provide conditions so that, using only static controls at the boundary, a certain target (a steady-state of the equation) is reached in infinite time. Applications of the main result are also presented, in particular, we provide several controllability results to heterogeneous equations of monostable and bistable types.</p>\",\"PeriodicalId\":48833,\"journal\":{\"name\":\"Evolution Equations and Control Theory\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolution Equations and Control Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/eect.2022035\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations and Control Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/eect.2022035","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
We are concerned with the controllability of a general heterogeneous semilinear parabolic equation of the form \begin{document}$ y_t(x,t)=y_{xx}(x,t)+f(x,y(x,t)) $\end{document} in one space dimension using boundary static controls. More precisely, we provide conditions so that, using only static controls at the boundary, a certain target (a steady-state of the equation) is reached in infinite time. Applications of the main result are also presented, in particular, we provide several controllability results to heterogeneous equations of monostable and bistable types.
A note on control of one-dimensional heterogeneous reaction-diffusion equations
We are concerned with the controllability of a general heterogeneous semilinear parabolic equation of the form \begin{document}$ y_t(x,t)=y_{xx}(x,t)+f(x,y(x,t)) $\end{document} in one space dimension using boundary static controls. More precisely, we provide conditions so that, using only static controls at the boundary, a certain target (a steady-state of the equation) is reached in infinite time. Applications of the main result are also presented, in particular, we provide several controllability results to heterogeneous equations of monostable and bistable types.
期刊介绍:
EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include:
* Modeling of physical systems as infinite-dimensional processes
* Direct problems such as existence, regularity and well-posedness
* Stability, long-time behavior and associated dynamical attractors
* Indirect problems such as exact controllability, reachability theory and inverse problems
* Optimization - including shape optimization - optimal control, game theory and calculus of variations
* Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s)
* Applications of the theory to physics, chemistry, engineering, economics, medicine and biology