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- Title
Controllability in Dimensions One and Two of Sobolev-Type Equations in Banach Spaces.
- Authors
Fedorov, V. E.; Ruzakova, O. A.
- Abstract
We establish conditions necessary for <MATH>\varepsilon</MATH>-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 <MATH>\varepsilon</MATH>-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 <MATH>\varepsilon</MATH>-controllability in dimension two of the Cauchy--Dirichlet problem for the Barenblatt--Zheltov--Kochina equation.
- Subjects
BANACH spaces; EQUATIONS; SOBOLEV spaces; COMPLEX variables
- Publication
Mathematical Notes, 2003, Vol 74, Issue 3/4, p583
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1023/A:1026160314352