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. 
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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/

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