Geodesic
Controllability in Dimensions One and Two of Sobolev-Type Equations in Banach Spaces
Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 618-628

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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. 
@article{MZM_2003_74_4_a14,
     author = {V. E. Fedorov and O. A. Ruzakova},
     title = {Controllability in {Dimensions} {One} and {Two} of {Sobolev-Type} {Equations} in {Banach} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {618--628},
     publisher = {mathdoc},
     volume = {74},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a14/}
}
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V. E. Fedorov; O. A. Ruzakova. Controllability in Dimensions One and Two of Sobolev-Type Equations in Banach Spaces. Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 618-628. http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a14/