摘要
We prove the null controllability in large time of the following linear parabolic equation involving the Grushin operator with an inverse-square potential $$u_t-\Delta_{x} u-|x|^{2}\Delta_{y}u-\frac{\mu}{|x|^2}u=v1_\omega$$in a bounded domain \({\Omega=\Omega_1\times \Omega_2\subset \mathbb{R}^{N_1} \times \mathbb{R}^{N_2} (N_1\geq 3, N_2\geq 1}\)) intersecting the surface {x = 0} under an additive control supported in an open subset \({\omega=\omega_1\times \Omega_2}\) of \({\Omega}\). Mathematics Subject Classification 93B05 93B07 35K65 35K67 Keywords Null controllability Uniform observability Grushin operator Hardy inequality Carleman inequality Dissipation speed Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (20) References1.D’Ambrosio L.: Hardy inequalities related to Grushin type operators. Proc. Am. Math. Soc 132, 725–734 (2003)CrossRefMATHMathSciNet2.Alabau-Boussouira F., Cannarsa P., Fragnelli G.: Carleman estimates for weakly degenerate parabolic operators with applications to null controllability. J. Evol. 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Anal. 254, 1864–1902 (2008)CrossRefMATHMathSciNet About this Article Title Null controllability in large time of a parabolic equation involving the Grushin operator with an inverse-square potential Journal Nonlinear Differential Equations and Applications NoDEA 23:20 Online DateApril 2016 DOI 10.1007/s00030-016-0364-3 Print ISSN 1021-9722 Online ISSN 1420-9004 Publisher Springer International Publishing Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Analysis Keywords 93B05 93B07 35K65 35K67 Null controllability Uniform observability Grushin operator Hardy inequality Carleman inequality Dissipation speed Authors Cung The Anh (1) Vu Manh Toi (2) Author Affiliations 1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam 2. Faculty of Computer Science and Engineering, Hanoi Water Resources University, 175 Tay Son, Dong Da, Hanoi, Vietnam Continue reading... 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