Null Controllability of Three-dimensional Heat Equation in Singular Domains
We study in this paper a class of parabolic equations in singular domains. These equations are defined in a singular cylindrical domain whose cross-section contains one reentrant corner or one straight emerging crack. We assume that the diffusion coefficients are non-smooth in the normal direction....
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| Veröffentlicht in: | Acta applicandae mathematicae 2014-12, Vol.134 (1), p.87-109 |
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| creator | Belghazi, A. H. |
| description | We study in this paper a class of parabolic equations in singular domains. These equations are defined in a singular cylindrical domain whose cross-section contains one reentrant corner or one straight emerging crack. We assume that the diffusion coefficients are non-smooth in the normal direction. We will show some
spectral inequality
thanks to Carleman type estimates and the construction of a suitable weight function satisfying some properties. As in Benabdallah et al. (C. R. Acad. Sci. Paris 344(6):357–362,
2007
), we deduce the null-controllability of these equations with the help of the Lebeau-Robbiano method. |
| doi_str_mv | 10.1007/s10440-014-9871-6 |
| format | Article |
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spectral inequality
thanks to Carleman type estimates and the construction of a suitable weight function satisfying some properties. As in Benabdallah et al. (C. R. Acad. Sci. Paris 344(6):357–362,
2007
), we deduce the null-controllability of these equations with the help of the Lebeau-Robbiano method.</description><identifier>ISSN: 0167-8019</identifier><identifier>EISSN: 1572-9036</identifier><identifier>DOI: 10.1007/s10440-014-9871-6</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Applications of Mathematics ; Calculus of Variations and Optimal Control; Optimization ; Computational Mathematics and Numerical Analysis ; Controllability ; Corners ; Cross sections ; Eigenvalues ; Estimates ; Heat conductivity ; Heat equations ; Inequalities ; Inequality ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Probability Theory and Stochastic Processes ; Spectra ; Studies ; Three dimensional ; Topological manifolds</subject><ispartof>Acta applicandae mathematicae, 2014-12, Vol.134 (1), p.87-109</ispartof><rights>Springer Science+Business Media Dordrecht 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c371t-67419ac513984c6283c93fbd83f5b6f041cd767b17b6ce0e6d06318428422cd53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10440-014-9871-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10440-014-9871-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Belghazi, A. H.</creatorcontrib><title>Null Controllability of Three-dimensional Heat Equation in Singular Domains</title><title>Acta applicandae mathematicae</title><addtitle>Acta Appl Math</addtitle><description>We study in this paper a class of parabolic equations in singular domains. These equations are defined in a singular cylindrical domain whose cross-section contains one reentrant corner or one straight emerging crack. We assume that the diffusion coefficients are non-smooth in the normal direction. We will show some
spectral inequality
thanks to Carleman type estimates and the construction of a suitable weight function satisfying some properties. As in Benabdallah et al. (C. R. Acad. Sci. Paris 344(6):357–362,
2007
), we deduce the null-controllability of these equations with the help of the Lebeau-Robbiano method.</description><subject>Applications of Mathematics</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Controllability</subject><subject>Corners</subject><subject>Cross sections</subject><subject>Eigenvalues</subject><subject>Estimates</subject><subject>Heat conductivity</subject><subject>Heat equations</subject><subject>Inequalities</subject><subject>Inequality</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Spectra</subject><subject>Studies</subject><subject>Three dimensional</subject><subject>Topological manifolds</subject><issn>0167-8019</issn><issn>1572-9036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kFFLwzAQx4MoOKcfwLeCL75E75o2aR9lTicOfXA-hzRNZ0bXbEn7sG9vRn0QQTg4Dn7_4-5HyDXCHQKI-4CQZUABM1oWAik_IRPMRUpLYPyUTAC5oAVgeU4uQtgAACs5n5DXt6Ftk5nreu_aVlW2tf0hcU2y-vLG0NpuTRes61SbLIzqk_l-UH2cE9slH7ZbD63yyaPbKtuFS3LWqDaYq58-JZ9P89VsQZfvzy-zhyXVTGBPuciwVDpHVhaZ5mnBdMmaqi5Yk1e8gQx1LbioUFRcGzC8Bs6wyNJYqa5zNiW3496dd_vBhF5ubdAmnt8ZNwSJPIIceJlG9OYPunGDj98cKYxuckQWKRwp7V0I3jRy5-1W-YNEkEe9ctQro1551Ct5zKRjJkS2Wxv_a_O_oW_gpXtk</recordid><startdate>20141201</startdate><enddate>20141201</enddate><creator>Belghazi, A. 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spectral inequality
thanks to Carleman type estimates and the construction of a suitable weight function satisfying some properties. As in Benabdallah et al. (C. R. Acad. Sci. Paris 344(6):357–362,
2007
), we deduce the null-controllability of these equations with the help of the Lebeau-Robbiano method.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10440-014-9871-6</doi><tpages>23</tpages></addata></record> |
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| subjects | Applications of Mathematics Calculus of Variations and Optimal Control Optimization Computational Mathematics and Numerical Analysis Controllability Corners Cross sections Eigenvalues Estimates Heat conductivity Heat equations Inequalities Inequality Mathematical analysis Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes Spectra Studies Three dimensional Topological manifolds |
| title | Null Controllability of Three-dimensional Heat Equation in Singular Domains |
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