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This article is cited in 11 scientific papers (total in 11 papers)
Controllability in Dimensions One and Two of Sobolev-Type Equations in Banach Spaces
V. E. Fedorov, O. A. Ruzakova Chelyabinsk State University
Abstract:
We establish conditions necessary for $\varepsilon$-controllability in dimension one of first-order singular linear differential equation in Banach spaces. This result generalizes similar results for regular equations. For this class of equations, we show that the notion of $\varepsilon$-controllability in dimension two is more natural, and moreover, analogous necessary conditions are sufficient in the case of dimension two. Using an abstract approach, we derive sufficient conditions for the $\varepsilon$-controllability in dimension two of the Cauchy–Dirichlet problem for the Barenblatt–Zheltov–Kochina equation.
Received: 15.01.2002 Revised: 19.09.2002
Citation:
V. E. Fedorov, O. A. Ruzakova, “Controllability in Dimensions One and Two of Sobolev-Type Equations in Banach Spaces”, Mat. Zametki, 74:4 (2003), 618–628; Math. Notes, 74:4 (2003), 583–592
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https://www.mathnet.ru/eng/mzm283https://doi.org/10.4213/mzm283 https://www.mathnet.ru/eng/mzm/v74/i4/p618
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Abstract page: | 353 | Full-text PDF : | 202 | References: | 46 | First page: | 1 |
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