Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type
نویسندگان
چکیده
منابع مشابه
Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type
The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator ∂ x + |x|∂ y (γ > 0) in the rectangle (x, y) ∈ (−1, 1)×(0, 1) or with the Kolmogorov-type operator v∂xf+∂ vf (γ ∈ {1, 2}) in the rectangle (x, v) ∈ T×(−1, 1), under an additive control supported in an open subset ω ...
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The null controllability of parabolic operators in bounded domains, with both boundary or locally distributed controls, is a well-established property, see, e.g., (Bensoussan et al., 1993) and (Fattorini, 1998). Such a property brakes down, however, for degenerate parabolic operators even when degeneracy occurs on ”small” subsets of the space domain, such as subsets of the boundary. This talk w...
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We study the null controllability of Kolmogorov-type equations ∂t f + v ∂x f − ∂2 v f = u(t, x, v)1ω(x, v) in a rectangle , under an additive control supported in an open subset ω of . For γ = 1, with periodic-type boundary conditions, we prove that null controllability holds in any positive time, with any control support ω. This improves the previous result by Beauchard and Zuazua (Ann Ins H P...
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In this paper we study controllability properties for semilinear degenerate parabolic equations with nonlinearities involving the first derivative in a bounded domain of R. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of ’regional null controllability’, showing that we can drive the solution to rest at time T on a subset of the sp...
متن کاملOn a class of degenerate parabolic equations of Kolmogorov type
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ژورنال
عنوان ژورنال: Séminaire Laurent Schwartz — EDP et applications
سال: 2014
ISSN: 2266-0607
DOI: 10.5802/slsedp.26